p}\left(\sqrt{p}n^{-\alpha}\right)+\mathcal{O}\left(\sqrt{p}\max\left(c_{n},pn^{-\beta},n^{-\gamma}\right)\right).$

By Assumptions C1 and D4, there exists a sample size
$n^{\ast}\in\mathbb{N}^{\ast}$ such that for all $n\in\mathbb{N}^{*}$
satisfying $n\geq n^{\ast}$ we have

$\Pr\left(\sup_{\bm{\theta}\in\bm{\Theta}}\;\Big{|}\hat{Q}(\bm{\theta},n)-Q(\bm{\theta})\Big{|}\geq\varepsilon\right)\leq\delta.$

Therefore, the four condition of Theorem 2.1 of Newey and McFadden (1994) are
verified implying the result.

∎

##  Appendix F Proof of Proposition 4

Without loss of generality we can assume that the sample sizes
$n^{*}\in\mathbb{N}^{*}$ of Assumption C3 and D5 are the same. Let
$n\in\mathbb{N}^{*}$ be such that $n\geq n^{*}$. By the definition of JIE in
(1), we have

$\hat{\bm{\pi}}\left({\bm{\theta}_{0}},n,{\bm{\omega}_{0}}\right)=\frac{1}{H}\sum_{h=1}^{H}\hat{\bm{\pi}}\left({\hat{\bm{\theta}}_{(j,n,H)}},n,\bm{\omega}_{h+jH}\right).$
(F.11)

Since the auxiliary estimator may be expressed, for any
$({\bm{\theta}},n,\bm{\omega})\in\bm{\Theta}\times\mathbb{N}^{*}\times\bm{\Omega}$,
as

$\hat{\bm{\pi}}\left({\bm{\theta}},n,{\bm{\omega}}\right)=\bm{\theta}+\mathbf{a}\left({\bm{\theta}}\right)+\mathbf{c}(n)+\mathbf{L}(n)\bm{\theta}+\mathbf{r}\left({\bm{\theta}},n\right)+\mathbf{v}\left({\bm{\theta}},n,{\bm{\omega}}\right).$
(F.12)

we deduce from (F.11), by using the mean value theorem on
$\mathbf{a}({\bm{\theta}})$ and $\mathbf{r}({\bm{\theta}},n)$, that

$\mathbf{B}\left({\bm{\theta}}^{(\mathbf{a},\mathbf{r})},n\right)\bm{\Delta}=\mathbf{v}\left({\bm{\theta}_{0}},n,{\bm{\omega}_{0}}\right)-\frac{1}{H}\sum_{h=1}^{H}\mathbf{v}\left({\hat{\bm{\theta}}_{(j,n,H)}},n,\bm{\omega}_{h+jH}\right),$
(F.13)

where
$\mathbf{B}\left({\bm{\theta}}^{(\mathbf{a},\mathbf{r})},n\right)\equiv\mathbf{I}+\mathbf{A}({\bm{\theta}}^{(\mathbf{a})})+\mathbf{L}(n)+\mathbf{R}\left({\bm{\theta}}^{(\mathbf{r})},n\right)$
and $\bm{\Delta}\equiv\hat{\bm{\theta}}_{(j,n,H)}-\bm{\theta}_{0}$. Applying
the mean value theorem on
$\mathbf{v}\left({\hat{\bm{\theta}}_{(j,n,H)}},n,{\bm{\omega}_{h+jH}}\right)$
we obtain for all $h=1,\dots,H$

$\mathbf{v}\left({\hat{\bm{\theta}}_{(j,n,H)}},n,{\bm{\omega}_{h+jH}}\right)=\mathbf{v}\left({\bm{\theta}_{0}},n,{\bm{\omega}_{h+jH}}\right)+\mathbf{V}\left({\bm{\theta}}^{(\mathbf{v})},n,\bm{\omega}_{h+jH}\right)\bm{\Delta}.$

Hence, let $\mathbf{u}\in{\rm I\\!R}^{p}$ be such that $||\mathbf{u}||_{2}=1$,
then by Assumption C3 we have,

$\sqrt{n}\mathbf{u}^{T}\bm{\Sigma}(\bm{\theta}_{0},n)^{-\nicefrac{{1}}{{2}}}\mathbf{v}\left({\bm{\theta}_{0}},n,{\bm{\omega}_{0}}\right)=Z(\bm{\theta}_{0},n,\bm{\omega}_{0},\mathbf{u})+\delta_{n}^{(1)}W(\bm{\theta}_{0},n,\bm{\omega}_{0},\mathbf{u})$

and for all $h=1,\dots,H$

$\sqrt{n}\mathbf{u}^{T}\bm{\Sigma}(\bm{\theta}_{0},n)^{-\nicefrac{{1}}{{2}}}\mathbf{v}\left({\bm{\theta}_{0}},n,{\bm{\omega}_{h+jH}}\right)=Z(\bm{\theta}_{0},n,\bm{\omega}_{h+jH},\mathbf{u})+\delta_{n}^{(h)}W(\bm{\theta}_{0},n,\bm{\omega}_{h+jH},\mathbf{u})$

where
$(\delta_{n}^{(0)}),(\delta_{n}^{(1)}),\dots,(\delta_{n}^{(H)})\in\mathfrak{D}$
and

$\displaystyle
Z(\bm{\theta}_{0},n,\bm{\omega}_{0},\mathbf{u})\sim\mathcal{N}(0,1),\;\;\;\;\;\;Z(\bm{\theta}_{0},n,\bm{\omega}_{h+jH},\mathbf{u})\sim\mathcal{N}(0,1),$
$\displaystyle
W(\bm{\theta}_{0},n,\bm{\omega}_{0},\mathbf{u})=\mathcal{O}_{\rm
p}(1),\;\;\;\;\;\;W(\bm{\theta}_{0},n,\bm{\omega}_{h+jH},\mathbf{u})=\mathcal{O}_{\rm
p}(1).$

Without loss of generality, we can suppose that
$(\delta_{n})\equiv(\delta_{n}^{(0)})=(\delta_{n}^{(1)})=\dots=(\delta_{n}^{(H)})$
as one may simply modify $W(\bm{\theta}_{0},n,\bm{\omega}_{0},\mathbf{u})$ and
$W(\bm{\theta}_{0},n,\bm{\omega}_{h+jH},\mathbf{u})$ for all $h=1,\dots,H$.
For simplicity, we write
$\mathfrak{X}_{\bm{\theta}_{0},n,\mathbf{u}}\equiv\sqrt{n}\mathbf{u}^{T}\bm{\Sigma}(\bm{\theta}_{0},n)^{-\nicefrac{{1}}{{2}}}$,
$Z_{0}\equiv Z(\bm{\theta}_{0},n,\bm{\omega}_{0},\mathbf{u})$ and $Z_{h}\equiv
Z(\bm{\theta}_{0},n,\bm{\omega}_{h+jH},\mathbf{u})$. Multiplying the right
hand side of (F.13) by $\mathfrak{X}_{\bm{\theta}_{0},n,\mathbf{u}}$, we have

$\displaystyle\mathfrak{X}_{\bm{\theta}_{0},n,\mathbf{u}}\left(\mathbf{v}\left({\bm{\theta}},n,{\bm{\omega}_{0}}\right)-\frac{1}{H}\sum_{h=1}^{H}\mathbf{v}\left({\hat{\bm{\theta}}_{(j,n,H)}},n,\bm{\omega}_{h+jH}\right)\right)$
(F.14) $\displaystyle=Z_{0}+\mathcal{O}_{\rm
p}(\delta_{n})-\dfrac{1}{H}\sum_{h=1}^{H}\big{(}Z_{h}+\mathcal{O}_{\rm
p}(\delta_{n})\big{)}-\dfrac{1}{H}\sum_{h=1}^{H}\mathfrak{X}_{\bm{\theta}_{0},n,\mathbf{u}}\mathbf{V}\left({\bm{\theta}}^{(\mathbf{v})},n,\bm{\omega}_{h+jH}\right)\bm{\Delta}$

The first two terms of (F.14) are considered separately in the following
computation

$\displaystyle Z_{0}+\mathcal{O}_{\rm
p}(\delta_{n})-\dfrac{1}{H}\sum_{h=1}^{H}\big{(}Z_{h}+\mathcal{O}_{\rm
p}(\delta_{n})\big{)}$
$\displaystyle=Z_{0}-\dfrac{1}{H}\sum_{h=1}^{H}Z_{h}+\mathcal{O}_{\rm
p}(\delta_{n})-\dfrac{1}{H}\sum_{h=1}^{H}\mathcal{O}_{\rm p}(\delta_{n})$
(F.15)
$\displaystyle\overset{d}{=}\left(1+\frac{1}{H}\right)^{\nicefrac{{1}}{{2}}}Z+\mathcal{O}_{\rm
p}(\delta_{n})-\mathcal{O}_{\rm p}\left(\frac{\delta_{n}}{\sqrt{H}}\right)$
$\displaystyle=\left(1+\frac{1}{H}\right)^{\nicefrac{{1}}{{2}}}Z+\mathcal{O}_{\rm
p}(\delta_{n}),$

where $Z\sim\mathcal{N}\left(0,1\right)$. We now consider the last term of
(F.14). Since
$\bm{\Sigma}({\bm{\theta}},n)^{-\nicefrac{{1}}{{2}}}=\mathcal{O}(1)$ and
$\mathbf{V}\left({\bm{\theta}}^{(\mathbf{v})},n,\bm{\omega}_{h+jH}\right)=\mathcal{O}_{p}\left(n^{-\nicefrac{{1}}{{2}}}\right)$
elementwise by Assumption C3 and $||\mathbf{u}||_{2}=1$ we have for all
$h=1,\dots,H$

$\mathfrak{X}_{\bm{\theta}_{0},n,\mathbf{u}}\mathbf{V}\left({\bm{\theta}}^{(\mathbf{v})},n,\bm{\omega}_{h+jH}\right)\bm{\Delta}=\mathcal{O}_{\rm
p}(p)\mathds{1}_{p}^{T}\bm{\Delta},$

where $\mathds{1}_{p}\in{\rm I\\!R}^{p}$ is the vector filled with ones. Since
Assumptions A2, B, C3 and D5 imply that $\hat{\bm{\theta}}_{(j,n,H)}$ is
consistent estimator of $\bm{\theta}_{0}$ (see Figure 1), there exists a
sequence $(\delta^{\prime}_{n})\in\mathfrak{D}$ such that
$\bm{\Delta}=\mathcal{O}_{\rm p}(\delta^{\prime}_{n})$ for all
$n\in\mathbb{N}^{*}$. Without loss of generality, we may assume that
$(\delta^{\prime}_{n})=(\delta_{n})$. Therefore, we have

$\displaystyle\mathfrak{X}_{\bm{\theta}_{0},n,\mathbf{u}}\mathbf{V}\left({\bm{\theta}}^{(\mathbf{v})},n,\bm{\omega}_{h+jH}\right)\bm{\Delta}$
$\displaystyle=\mathcal{O}_{\rm
p}(p)\mathds{1}_{p}^{T}\bm{\Delta}=\mathcal{O}_{\rm
p}(p)\mathds{1}_{p}^{T}\mathcal{O}_{\rm p}(\delta_{n})\mathds{1}_{p}$
$\displaystyle=\mathcal{O}_{\rm
p}(p\delta_{n})\mathds{1}_{p}^{T}\mathds{1}_{p}=\mathcal{O}_{\rm
p}(p^{2}\delta_{n}),$

which leads to the computation for the last term of (F.14),

$\dfrac{1}{H}\sum_{h=1}^{H}\mathfrak{X}_{\bm{\theta}_{0},n,\mathbf{u}}\mathbf{V}\left({\bm{\theta}}^{(\mathbf{v})},n,\bm{\omega}_{h+jH}\right)\bm{\Delta}=\dfrac{1}{H}\sum_{h=1}^{H}\mathcal{O}_{\rm
p}(p^{2}\delta_{n})=\mathcal{O}_{\rm
p}\left(\delta_{n}\frac{p^{2}}{\sqrt{H}}\right).$ (F.16)

Combining (F.13), (F.14) and (F.16), we obtain

$\displaystyle\left(1+\frac{1}{H}\right)^{-\nicefrac{{1}}{{2}}}\mathfrak{X}_{\bm{\theta}_{0},n,\mathbf{u}}\mathbf{B}\left({\bm{\theta}}^{(\mathbf{a},\mathbf{r})},n\right)\bm{\Delta}$
$\displaystyle=$
$\displaystyle\left(1+\frac{1}{H}\right)^{-\nicefrac{{1}}{{2}}}\mathfrak{X}_{\bm{\theta}_{0},n,\mathbf{u}}\left(\mathbf{v}\left({\bm{\theta}},n,{\bm{\omega}_{0}}\right)-\frac{1}{H}\sum_{h=1}^{H}\mathbf{v}\left({\hat{\bm{\theta}}_{(j,n,H)}},n,\bm{\omega}_{h+jH}\right)\right)$
$\displaystyle\overset{d}{=}\left(1+\frac{1}{H}\right)^{-\nicefrac{{1}}{{2}}}\left(\left(1+\frac{1}{H}\right)^{\nicefrac{{1}}{{2}}}Z+\mathcal{O}_{\rm
p}(\delta_{n})+\mathcal{O}_{\rm
p}\left(\delta_{n}\frac{p^{2}}{\sqrt{H}}\right)\right)$
$\displaystyle\overset{d}{=}Z+\mathcal{O}_{\rm
p}\left(\delta_{n}\sqrt{\frac{H}{H+1}}\right)+\mathcal{O}_{\rm
p}\left(\delta_{n}\frac{p^{2}}{\sqrt{H+1}}\right)$
$\displaystyle=Z+\delta_{n}\mathcal{O}_{\rm
p}\left(1\right)+\delta_{n}\mathcal{O}_{\rm
p}\left(\frac{p^{2}}{\sqrt{H}}\right)=Z+\delta_{n}\mathcal{O}_{\rm
p}\left(\max\left(1,\frac{p^{2}}{\sqrt{H}}\right)\right).$

The proof is completed using (11) of Assumption D5.

∎

## References

  * Adimari and Ventura (2001) G. Adimari and L. Ventura.  Robust inference for generalized linear models with application to logistic regression.  _Statistics and Probability Letters_ , 55:413–419, 2001\.
  * Albert and Anderson (1984) A. Albert and J. A. Anderson.  On the existence of maximum likelihood estimates in logistic regression models.  _Biometrika_ , 71:1–10, 1984.
  * Austin and Steyerberg (2017) P. C. Austin and E. W. Steyerberg.  Events per variable (EPV) and the relative performance of different strategies for estimating the out-of-sample validity of logistic regression models.  _Statistical Methods in Medical Research_ , 26:796–808, 2017.
  * Barndorff-Nielsen (1983) O. Barndorff-Nielsen.  On a formula for the distribution of the maximum likelihood estimator.  _Biometrika_ , 70:343–365, 1983.
  * Barnwal and Paul (1988) R. K. Barnwal and S. R. Paul.  Analysis of one-way layout of count data with negative binomial variation.  _Biometrika_ , 75:215–222, 1988.
  * Bartolucci et al. (2016) F. Bartolucci, R. Bellio, A. Salvan, and N. Sartori.  Modified profile likelihood for fixed-effects panel data models.  _Econometric Reviews_ , 35:1271–1289, 2016.
  * Basu et al. (1998) A. Basu, I. R Harris, N. L. Hjort, and M. C. Jones.  Robust and efficient estimation by minimising a density power divergence.  _Biometrika_ , 85:549–559, 1998.
  * Bellio and Sartori (2006) R. Bellio and N. Sartori.  Practical use of modified maximum likelihoods for stratified data.  _Biometrical Journal_ , 48:876–886, 2006.
  * Belloni et al. (2015) A. Belloni, V. Chernozhukov, and K. Kato.  Uniform post-selection inference for least absolute deviation regression and other Z-estimation problems.  _Biometrika_ , 102:77–94, 2015.
  * Bergesio and Yohai (2011) A. Bergesio and V. J. Yohai.  Projection estimators for generalized linear models.  _Journal of the American Statistical Association_ , 106:661–671, 2011.
  * Bester and Hansen (2009) C. A. Bester and C. Hansen.  A penalty function approach to bias reduction in nonlinear panel models with fixed effects.  _Journal of Business and Economic Statistics_ , 27:131–148, 2009.
  * Bianco and Yohai (1996) A. M. Bianco and V. J. Yohai.  Robust estimation in the logistic regression model.  In H. Reider, editor, _Robust statistics, Data analysis and computer intensive methods_ , pages 17–34. Springer Verlag, New York, 1996.
  * Bickel et al. (2009) P. J. Bickel, Y. Ritov, and A. B. Tsybakov.  Simultaneous analysis of lasso and dantzig selector.  _The Annals of Statistics_ , 37:1705–1732, 2009.
  * Bondell (2005) H. D. Bondell.  Minimum distance estimation for the logistic regression model.  _Biometrika_ , 92:724–731, 2005.
  * Botter and Cordeiro (1998) D. A. Botter and M. D. Cordeiro.  Improved estimators for generalized linear models with dispersion covariates.  _Journal of Statistical Computation and Simulation_ , 62:91–104, 1998.
  * Brazzale et al. (2007) A. R. Brazzale, A. C. Davison, and N. Reid.  _Applied Asymptotics_.  Cambridge University Press, Cambridge, 2007.
  * Breslow (1984) N. E. Breslow.  Extra-Poisson variation in log-linear models.  _Journal of the Royal Statistical Society, Series C_ , 33:38–44, 1984.
  * Breslow and Clayton (1993) N. E. Breslow and D. G. Clayton.  Approximate inference in generalized linear mixed models.  _JASA_ , 88:9–25, 1993.
  * Bühlmann (2013) P. Bühlmann.  Statistical significance in high-dimensional linear models.  _Bernoulli_ , 19:1212–1242, 2013.
  * Bühlmann and Mandozzi (2014) P. Bühlmann and J. Mandozzi.  High-dimensional variable screening and bias in subsequent inference, with an empirical comparison.  _Computational Statistics_ , 29:407–430, 2014.
  * Bühlmann and van de Geer (2011) P. Bühlmann and S. A. van de Geer.  _Statistics for High-dimensional Data_.  Springer, Berlin, 2011.
  * Bull et al. (1997) S. B. Bull, C. M. T. Greenwood, and W. W. Hauck.  Jackknife bias reduction for polychotomous logistic regression.  _Statistics in Medicine_ , 16(5):545–560, 1997\.
  * Bull et al. (2002a) S. B. Bull, C. Mak, and C. M. T. Greenwood.  A modified score function estimator for multinomial logistic regression in small samples.  _Computational Statistics and Data Analysis_ , 39:57–74, 2002a.
  * Bull et al. (2002b) S. B. Bull, C. Mak, and C. M. T. Greenwood.  A modified score function estimator for multinomial logistic regression in small samples.  _Computational Statistics and Data Analysis_ , 39:57–74, 2002b.
  * Bull et al. (2007) S. B. Bull, J. P. Lewinger, and S. S. F. Lee.  Confidence intervals for multinomial logistic regression in sparse data.  _Statistics in Medicine_ , 26:903–918, 2007.
  * Byers et al. (2003) A. L. Byers, H. Allore, T. M. Gill, and P. N. Peduzzi.  Application of negative binomial modeling for discrete outcomes: a case study in aging research.  _Journal of Clinical Epidemiology_ , 56:559–564, 2003.
  * Cadigan and Bataineh (2012) N. G. Cadigan and O. M. Bataineh.  Inference about the ratio of means from negative binomial paired count data.  _Environmental and Ecological Statistics_ , 19:269–293, 2012.
  * Cameron and Trivedi (2013) A. C. Cameron and P. K. Trivedi.  _Regression Analysis of Count Data, 2nd edition_.  Number 53 in Econometric Society Monograph. Cambridge University Press, Cambridge, UK, 2013.
  * Candès and Sur (2018) E. J. Candès and P. Sur.  The phase transition for the existence of the maximum likelihood estimate in high-dimensional logistic regression.  Technical report, Stanford University, Stanford, CA 94305, USA, 2018.  Working paper available at: https: // arxiv. org/ pdf/ 1804. 09753. pdf.
  * Cantoni and Ronchetti (2001) E. Cantoni and E. Ronchetti.  Robust inference for generalized linear models.  _Journal of the American Statistical Association_ , 96:1022–1030, 2001.
  * Carroll and Pederson (1993) R. J. Carroll and S. Pederson.  On robustness in the logistic regression model.  _Journal of the Royal Statistical Society, Series B_ , 55:693–706, 1993.
  * Castilla et al. (2018) E. Castilla, A. Ghosh, N. Martin, and L. Pardo.  New robust statistical procedures for the polytomous logistic regression models.  _Biometrics_ , 2018.  To appear.
  * Choi et al. (2000) E. Choi, P. Hall, and B. Presnell.  Rendering parametric procedures more robust by empirically tilting the model.  _Biometrika_ , 87:453–465, 2000.
  * Christmann (1994) A. Christmann.  Least median of weighted squares in logistic regression with large strata.  _Biometrika_ , 81:413–417, 1994.
  * Christmann and Rousseeuw (2001) A. Christmann and P. J. Rousseeuw.  Measuring overlap in binary regression.  _Computational Statistics and Data Analysis_ , 37:65–75, 2001.
  * Cíźek (2008) P. Cíźek.  Robust and efficient adaptive estimation of binary-choice regression models.  _Journal of the American Statistical Association_ , 103:687–.696, 2008.
  * Consul (1989) P. C. Consul.  _Generalized Poisson Distributions_.  Marcel Dekker, New York, 1989.
  * Cook et al. (1986) R. D. Cook, C.-L. Tsai, and B. C. Wei.  Bias in nonlinear regression.  _Biometrika_ , 73:615–623, 1986.
  * Copas (1988) J. B. Copas.  Binary regression models for contaminated data.  _Journal of the Royal Statistical Society, Series B_ , 50:225–265, 1988.
  * Cordeiro and Botter (2001) G. M. Cordeiro and D. A. Botter.  Second-order biases of maximum likelihood estimates in overdispersed generalized linear models.  _Statistics & Probability Letters_, 55:269–280, 2001\.
  * Cordeiro and McCullagh (1991) G. M. Cordeiro and P. McCullagh.  Bias correction in generalized linear models.  _Journal of the Royal Statistical Society, Series B_ , 53:629–643, 1991.
  * Cordeiro and Toyama Udo (2008) G. M. Cordeiro and M. C. Toyama Udo.  Bias correction in generalized nonlinear models with dispersion covariates.  _Communications in Statistics - Theory and Methods_ , 37:2219–2225, 2008.
  * Cordeiro and Vasconcellos (1997) G. M. Cordeiro and K. L. P. Vasconcellos.  Bias correction for a class of multivariate nonlinear regression models.  _Statistics and Probability Letters_ , 35:155–164, 1997\.
  * Courvoisier et al. (2011) D. S. Courvoisier, C. Combescure, T. Agoritsas, A. Gayet-Ageron, and T. V. Perneger.  Performance of logistic regression modeling: beyond the number of events per variable, the role of data structure.  _Journal of Clinical Epidemiology_ , 64:993–1000, 2011\.
  * Cox (2006) D. R. Cox.  _Principles of statistical inference_.  Cambridge University Press, Cambridge, 2006.
  * Cox and Snell (1968) D. R. Cox and E. J. Snell.  A general definition of residuals.  _Journal of the Royal Statistical Society, Series B_ , 30:248–275, 1968.
  * Croux and Haesbroeck (2003) C. Croux and G. Haesbroeck.  Implementing the Bianco and Yohai estimator for logistic regression.  _Computational Statistics and Data Analysis_ , 44:273–295, 2003.
  * Dezeure et al. (2015) R. Dezeure, P. Bühlmann, L. Meier, and N. Meinshausen.  High-dimensional inference: Confidence intervals, $p$-values and r-software hdi.  _Statistical Science_ , 30:533–558, 2015.
  * Dezeure et al. (2017) R. Dezeure, P. Bühlmann, and C.-H. Zhang.  High-dimensional simultaneous inference with the bootstrap.  _TEST_ , 26:685–719, 2017.
  * DiCiccio et al. (1996) T. J. DiCiccio, M. A. Martin, S. E. Stern, and G. A. Young.  Information bias and adjusted profile likelihoods.  _Journal of the Royal Statistical Society, Series B_ , 58:189–203, 1996.
  * Duffie and Singleton (1993) D. Duffie and K. J. Singleton.  Simulated moments estimation of markov models of asset prices.  _Econometrica: Journal of the Econometric Society_ , pages 929–952, 1993.
  * Efron (1975) B. Efron.  Defining the curvature of a statistical problem (with applications to second order efficiency).  _The Annals of Statistics_ , 3:1189–1242, 1975.
  * Efron (1979) B. Efron.  Bootstrap methods: Another look at the jackknife.  _The Annals of Statistics_ , 7:1–26, 1979.
  * Efron (1982) B. Efron.  _The Jackknife, the Bootstrap an Other Resampling Plans_ , volume 38.  Society for Industrial an Applied Mathematics, Philadelphia, 1982.
  * Efron and Tibshirani (1994) B. Efron and R. J. Tibshirani.  _An introduction to the bootstrap_.  CRC press, 1994.
  * Engel (1984) J. Engel.  Models for response data showing extra-Poisson variation.  _Statistica Neerlandica_ , 38:159–167, 1984.
  * Ferguson et al. (1991) H. Ferguson, N. Reid, and D. R. Cox.  Estimating equations from modified profile likelihood.  In V. P. Godambe, editor, _Estimating Functions_ , pages 279–93. Clarendon Press, Oxford, 1991.
  * Firth (1993) D. Firth.  Bias reduction of maximum likelihood estimates.  _Biometrika_ , 80:27–38, 1993.
  * Gallant and Long (1997) A. R. Gallant and J. R. Long.  Estimating stochastic differential equations efficiently by minimum Chi-squared.  _Biometrika_ , 84:125–141, 1997.
  * Gallant and Tauchen (1996) A Ronald Gallant and George Tauchen.  Which moments to match?  _Econometric Theory_ , pages 657–681, 1996.
  * Gart et al. (1985) J. J. Gart, H. M. Pettigrew, and D. G. Thomas.  The effect of bias, variance estimation, skewness and kurtosis of the empirical logit on weighted least squares analyses.  _Biometrika_ , 72:179–190, 1985.
  * Gelman et al. (2008) A. Gelman, A. Jakulin, M. G. Pittau, and Y.-S. Su.  A weakly informative default prior distribution for logistic and other regression models.  _The Annals of Applied Statistics_ , 2:1360–1383, 2008\.
  * Genton and de Luna (2000) M. G. Genton and X. de Luna.  Robust simulation-based estimation.  _Statistics & probability letters_, 48(3):253–259, 2000.
  * Gervini (2005) D. Gervini.  Robust adaptive estimators for binary regression models.  _Journal of Statistical Planning and Inference_ , 131:297–311, 2005.
  * Ghosh et al. (2016) A. Ghosh, , and A. Basu.  Robust estimation in generalized linear models: the density power divergence approach.  _TEST_ , 25:269–290, 2016.
  * Gourieroux et al. (1993) C. Gourieroux, A. Monfort, and E. Renault.  Indirect inference.  _Journal of applied econometrics_ , 8(S1):S85–S118, 1993.
  * Greenland (2000) S. Greenland.  Small-sample bias and corrections for conditional maximum-likelihood odds-ratio estimators.  _Biostatistics_ , 1:113–122, 2000.
  * Greenland and Mansournia (2015) S. Greenland and M. A. Mansournia.  Penalization, bias reduction, and default priors in logistic and related categorical and survival regressions.  _Statistics in Medicine_ , 34:3133–3143, 2015.
  * Greenland et al. (2016) S. Greenland, M. A. Mansournia, and D. G. Altman.  Sparse data bias: a problem hiding in plain sight.  _BMC medical research methodology_ , 352, 2016.
  * Greenshtein and Ritov (2004) E. Greenshtein and Y. Ritov.  Persistence in high-dimensional linear predictor selection and the virtue of overparametrization.  _Bernoulli_ , 10:971–988, 2004.
  * Greenwood and Yule (1920) M. Greenwood and G. U. Yule.  An inquiry into the nature of frequency distributions of multiple happenings, with particular reference to the occurrence of multiple attacks of disease or repeated accidents.  _Journal of the Royal Statistical Society, Series A_ , 83:255–279, 1920.
  * Guerrier et al. (2018) S. Guerrier, E. Dupuis-Lozeron, Y. Ma, and M.-P. Victoria-Feser.  Simulation-based bias correction methods for complex models.  _Journal of the American Statistical Association_ , pages 1–12, 2018\.
  * Hall (2005) A. R. Hall.  _Generalized Method of Moments_.  Advanced Texts in Econometrics. Oxford University Press, Oxford, 2005\.
  * Hall and Martin (1988) P. Hall and M. A. Martin.  On bootstrap resampling and iteration.  _Biometrika_ , 75(4):661–671, 1988.
  * Hampel et al. (1986) F. R. Hampel, E. Ronchetti, P. J. Rousseeuw, and W. A. Stahel.  _Robust Statistics: The Approach Based on Influence Functions_.  John Wiley, New York, 1986.
  * Hansen (1982) L. P. Hansen.  Large sample properties of generalized method of moments estimators.  _Econometrica_ , 50:1029–1054, 1982.
  * Heinze (2006) G. Heinze.  A comparative investigation of methods for logistic regression with separated or nearly separated data.  _Statistics in medicine_ , 25:4216–4226, 2006.
  * Heinze and Puhr (2010) G. Heinze and R. Puhr.  Bias-reduced and separation-proof conditional logistic regression with small or sparse data sets.  _Statistics in Medicine_ , 29:770–777, 2010.
  * Heinze and Schemper (2002) G. Heinze and M. Schemper.  A solution to the problem of separation in logistic regression.  _Statistics in Medicine_ , 21:2409–2419, 2002.
  * Heller et al. (2018) G. Z. Heller, D.-L. Couturier, and S. R. Heritier.  Beyond mean modelling: Bias due to misspecification of dispersion in Poisson-inverse Gaussian regression.  _Biometrical Journal_ , 2018.  Online version.
  * Heritier et al. (2009) S. Heritier, E. Cantoni, S. Copt, and M.P. Victoria-Feser.  _Robust Methods in Biostatistics_.  Wiley, 2009.
  * Hilbe (2011) J. M. Hilbe.  _Negative binomial regression (2nd ed.)_.  Cambridge University Press, New York, 2011.
  * Hilbe (2014) J. M. Hilbe.  _Modeling Count Data_.  Cambridge University Press, Cambridge, UK, 2014.
  * Hirji et al. (1989) K. F. Hirji, A. A. Tsiatis, and C. R. Mehta.  Median unbiased estimation for binary data.  _The American Statistician_ , 43:7–11, 1989.
  * Hobza et al. (2008) T. Hobza, L. Pardo, and I. Vajda.  Robust median estimator in logistic regression.  _Journal of Statistical Planning and Inference_ , 138:3822–3840, 2008.
  * Hoerl and Kennard (1970) A. E. Hoerl and R. Kennard.  Ridge regression: Biased estimation for nonorthogonal problems.  _Technometrics_ , 12:55–67, 1970.
  * Hosseinian and Morgenthaler (2011) S. Hosseinian and S. Morgenthaler.  Robust binary regression.  _Journal of Statistical Planning and Inference_ , 141:1497–1509, 2011.
  * Huber et al. (2004) P. Huber, E. Ronchetti, and M.-P. Victoria-Feser.  Estimation of generalized linear latent variable models.  _Journal of the Royal Statistical Society, Series B_ , 66(4):893–908, 2004.
  * Huber (1981) P. J. Huber.  _Robust Statistics_.  John Wiley, New York, 1981.
  * Huber (1964) Peter J Huber.  Robust estimation of a location parameter.  _The Annals of Mathematical Statistics_ , 35(1):73–101, 1964.
  * Huber and Ronchetti (2009) P.J. Huber and E.M. Ronchetti.  _Robust Statistics_.  Wiley Series in Probability and Statistics. John Wiley and Sons, Hoboken, 2009.  2nd Edition.
  * Javanmard and Montanari (2014) A. Javanmard and A. Montanari.  Confidence intervals and hypothesis testing for high-dimensional regression.  _Journal of Machine Learning Research_ , 15:2869–2909, 2014\.
  * Jeffreys (1946) H. Jeffreys.  An invariant form for the prior probability in estimation problems.  _Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences_ , 186(1007):453–461, 1946\.
  * Joe and Zhu (2005) H. Joe and R. Zhu.  Generalized Poisson distribution: the property of mixture of Poisson and comparison with negative binomial distribution.  _Biometrical journal_ , 47:219–229, 2005.
  * Jorgensen (1997) B. Jorgensen.  _The Theory of Dispersion Models_.  Chapman & Hall, London, 1997.
  * Jorgensen and J. (2004) B. Jorgensen and Knudsen S. J.  Parameter orthogonality and bias adjustment for estimating functions.  _Scandinavian Journal of Statistics_ , 31:93–114, 2004\.
  * Karlis and Xekalaki (2005) D. Karlis and E. Xekalaki.  Mixed Poisson distributions.  _International Statistical Review_ , 73:35–58, 2005.
  * Kenne Pagui et al. (2017) E. C. Kenne Pagui, A. Salvan, and N. Sartori.  Median bias reduction of maximum likelihood estimates.  _Biometrika_ , 104:923–938, 2017.
  * Kolassa (1997) J. E. Kolassa.  Infinite parameter estimates in logistic regression, with application to approximate conditional inference.  _Scandinavian Journal of Statistics_ , 24:523–530, 1997\.
  * Kordzakhia et al. (2001) N. Kordzakhia, G. D. Mishra, and L. Reiersolmoen.  Robust estimation in the logistic regression mode.  _Journal of Statistical Planning and Inference_ , 98:211—223, 2001.
  * Kosmidis (2014a) I. Kosmidis.  Improved estimation in cumulative link models.  _Journal of the Royal Statistical Society, Series B_ , 76:169–196, 2014a.
  * Kosmidis (2014b) I. Kosmidis.  Bias in parametric estimation: reduction and useful side-effects.  _Wiley Interdisciplinary Reviews: Computational Statistics_ , 6(3):185–196, 2014b.
  * Kosmidis (2017) I. Kosmidis.  _brglm: Bias Reduction in Binary-Response Generalized Linear Models_ , 2017.  URL http://www.ucl.ac.uk/~ucakiko/software.html.  R package version 0.6.1.
  * Kosmidis and Firth (2009) I. Kosmidis and D. Firth.  Bias reduction in exponential family nonlinear models.  _Biometrika_ , 96:793–804, 2009.
  * Kosmidis and Firth (2010) I. Kosmidis and D. Firth.  A generic algorithm for reducing bias in parametric estimation.  _Electronic Journal of Statistics_ , 4:1097–1112, 2010\.
  * Kosmidis and Firth (2011) I. Kosmidis and F. Firth.  Multinomial logit bias reduction via the Poisson log-linear model.  _Biometrika_ , 98:755–759, 2011.
  * Kosmidis et al. (2017) I. Kosmidis, A. Guolo, and C. Varin.  Improving the accuracy of likelihood-based inference in meta-analysis and meta-regression.  _Biometrika_ , 104:489–496, 2017.
  * Krishna (2011) K. S. Krishna.  Interval estimation of the over-dispersion parameter in the analysis of one-way layout of count data.  _Statistics in Medicine_ , 30:39–51, 2011.
  * Kuensch et al. (1989) H. R. Kuensch, L. A. Stefanski, and R. J. Carroll.  Conditionally unbiased bounded-influence estimation in general regressionmodels, with applications to generalized linear models.  _Journal of the American Statistical Association_ , 84:460–466, 1989.
  * Kuk (1995) A. Y. C. Kuk.  Asymptotically unbiased estimation in generalized linear models with random effects.  _Journal of the Royal Statistical Society. Series B (Methodological)_ , pages 395–407, 1995.
  * Kyriakou et al. (2018) S. Kyriakou, I. Kosmidis, and N. Sartori.  Median bias reduction in random-effects meta-analysis and meta-regression.  _Statistical Methods in Medical Research_ , 2018.  In press.
  * Lawless (1987) J. F. Lawless.  Negative binomial and mixed Poisson regression.  _Canadian Journal of Statistics_ , 15:209–225, 1987.
  * Le Cessie (1992) J. C. Le Cessie, S. andVan Houwelingen.  Ridge estimators in logistic regression.  _Journal of the Royal Statistical Society, Series C_ , 41:191–201, 1992.
  * Leng et al. (2006) C. Leng, Y. Lin, and G. Wahba.  A note on the lasso and related procedures in model selection.  _Statistica Sinica_ , 16:1273–1284, 2006.
  * Lesaffre and Albert (1989) E. Lesaffre and A. Albert.  Partial separation in logistic discrimination.  _Journal of the Royal Statistical Society, Series B_ , 51:109–116, 1989.
  * Li (2017) S. Li.  Debiasing the debiased lasso with bootstrap.  Technical report, Department of Statistics and Biostatistics, Rutgers University, 2017.  Working paper available at: https://arXiv:1711.03613v1.
  * Lin and Breslow (1996) X. Lin and N. E. Breslow.  Bias correction in generalized linear mixed models with multiple componentsof dispersion.  _Journal of the American Statistical Association_ , 91:1007–1016, 1996.
  * Lloyd-Smith (2007) J. O. Lloyd-Smith.  Maximum likelihood estimation of the negative binomial dispersion parameter for highly overdispersed data, with applications to infectious diseases.  _PLoS ONE_ , 2, 2007.
  * Lloyd-Smith et al. (2005) J. O. Lloyd-Smith, S. J. Schreiber, P. E. Kopp, and W. M. Getz.  Superspreading and the effect of individual variation on disease emergence.  _Nature_ , 438:355–359, 2005.
  * Lockhart et al. (2014) R. Lockhart, J. Taylor, R. J. Tibshirani, and R. Tibshirani.  A significance test for the lasso.  _The Annals of Statistics_ , 42:413–468, 2014.
  * Lyles et al. (2012) R. H. Lyles, Y. Guo, and S. Greenland.  Reducing bias and mean squared error associated with regression-based odds ratio estimators.  _Journal of Statistical Planning and Inference_ , 142:3235–3241, 2012.
  * M. C. Jones et al. (2001) M. C. M. C. Jones, N. L. Hjort, I. R. Harris, and A. Basu.  A comparison of related density-based minimum divergence estimators.  _Biometrika_ , 88:865–873, 2001.
  * Maechler et al. (2018) M. Maechler, P. Rousseeuw, C. Croux, V. Todorov, A. Ruckstuhl, M. Salibian-Barrera, T. Verbeke, M. Koller, E. L. T. Conceicao, and M. Anna di Palma.  _robustbase: Basic Robust Statistics_ , 2018.  URL http://robustbase.r-forge.r-project.org/.  R package version 0.93-2.
  * Manton et al. (1981) G. Manton, K, M. A. Woodbury, and E. Stallard.  A variance components approach to categorical data models with heterogenous cell populations: Analysis of spatial gradients in lung cancer mortality rates in North Carolina counties.  _Biometrics_ , 37:259–269, 1981.
  * Markatou et al. (1997) M. Markatou, A. Basu, and B. Lindsay.  Weighted likelihood estimating equations: The discrete case with applicationsto logistic regression.  _Journal of Statistical Planning and Inference_ , 57:215–232, 1997.
  * Maronna et al. (2006) R. A. Maronna, R. D. Martin, and V. J. Yohai.  _Robust Statistics: Theory and Methods_.  Wiley, Chichester, West Sussex, UK, 2006.
  * McCullagh and Nelder (1989) P. McCullagh and J. A. Nelder.  _Generalized Linear Models_.  Chapman and Hall, London, 1989.  Second edition.
  * McFadden (1989) D. McFadden.  A method of simulated moments for estimation of discrete response models without numerical integration.  _Econometrica: Journal of the Econometric Society_ , pages 995–1026, 1989.
  * Mehrabi and Matthews (1995) Y. Mehrabi and J. N. S. Matthews.  Likelihood-based methods for bias reduction in limiting dilution assays.  _Biometrics_ , 51:1543–1549, 1995.
  * Meinchausen (2015) N. Meinchausen.  Group-bound: Confidence intervals for groups of variables in sparse high-dimensional regression without assumptions on the design.  _Journal of the Royal Statistical Society, Series B._ , 77:923–945, 2015.
  * Meinshausen and Bühlmann (2010) N. Meinshausen and P. Bühlmann.  Stability selection.  _Journal of the Royal Statistical Society: Series B_ , 72:417–473, 2010.
  * Meinshausen et al. (2009) N. Meinshausen, L. Meier, and P. Bühlmann.  p-values for high-dimensional regression.  _Journal of the American Statistical Association_ , 104:1671–1681, 2009.
  * Morgenthaler (1992) S. Morgenthaler.  Least-absolute-deviations fits for generalized linear models.  _Biometrika_ , 79:747–754, 1992.
  * Nelder and Wedderburn (1972) J. Nelder and R. Wedderburn.  Generalized linear models.  _Journal of the Royal Statistical Society, Series A_ , 135:370–384, 1972.
  * Newey and McFadden (1994) W. K. Newey and D. McFadden.  Large sample estimation and hypothesis testing.  _Handbook of econometrics_ , 4:2111–2245, 1994.
  * Nikoloulopoulos and Karlis (2008) A. K. Nikoloulopoulos and D. Karlis.  On modeling count data: a comparison of some well-known discrete distributions.  _Journal of Statistical Computation and Simulation_ , 78:437–457, 2008.
  * Pace and Salvan (2006) L. Pace and A. Salvan.  Adjustments of the profile likelihood from a new perspective.  _Journal of Statistical Planning and Inference_ , 136:3554–3564, 2006.
  * Paul and Banerjee (1998) S. R. Paul and T. Banerjee.  Analysis of two-way layout of count data involving multiple counts in each cell.  _Journal of the American Statistical Association_ , 93:1419–1429, 1998.
  * Paul and Saha (2007) S. R. Paul and K. K. Saha.  The generalized linear model and extensions: a review and some biological and environmental applications.  _Environmetrics_ , 18:421–443, 2007.
  * Pavlou et al. (2015) M. Pavlou, G. Ambler, S. R. Seaman, O. Guttmann, P. Elliott, M. King, and R. Z. Omar.  How to develop a more accurate risk prediction model when there are few events.  _BMC medical research methodology_ , 351, 2015.
  * Pavlou et al. (2016) M. G. Pavlou, G.r Amble, S. R. Seaman, M. De Iorio, and R. Z. Omar.  Review and evaluation of penalised regression methods for risk prediction in low‐dimensional data with few events.  _Statistics in medicine_ , 35:1159–1177, 2016.
  * Peduzzi et al. (1996) P. Peduzzi, J. Concato, E. Kemper, T. R. Holford, and A. R. Feinstein.  A simulation study of the number of events per variable in logistic regression analysis.  _Journal of Clinical Epidemiology_ , 49:1373–1379, 1996\.
  * Pettitt et al. (1998) A. N. Pettitt, J. M. Kelly, and J. T. Gao.  Bias correction for censored data with exponential lifetimes.  _Statistica Sinica_ , 8:941–963, 1998.
  * Piegorsch (1990) W. W. Piegorsch.  Maximum likelihood estimation for the negative binomial dispersion parameter.  _Biometrics_ , 46:863–867, 1990.
  * Pregibon (1981) D. Pregibon.  Logistic regression diagnostics.  _The Annals of Statistics_ , 9:705–724, 1981.
  * Pregibon (1982) D. Pregibon.  Resistant fits for some commonly used logistic models with medical applications.  _Biometrics_ , 38:485–498, 1982.
  * Puhr et al. (2017) R. Puhr, G. Heinze, M. Nold, L. Lusa, and A. Geroldinger.  Firth’s logistic regression with rare events: accurate effect estimates and predictions?  _Statistics in Medicine_ , 36:2302–2317, 2017.
  * Rahman and Sultana (2017) M. S. Rahman and M. Sultana.  Performance of Firth-and logf-type penalized methods in risk prediction for small or sparse binary data.  _BMC medical research methodology_ , 2017.
  * Rigby et al. (2008) R. A. Rigby, D. M. Stasinopoulos, and C. Akantziliotou.  A framework for modelling overdispersed count data, including the Poisson-shifted generalized inverse Gaussian distribution.  _Computational Statistics & Data Analysis_, 53:381–393, 2008.
  * Rizopoulos et al. (2009) D. Rizopoulos, G. Verbeke, and E. Lesaffre.  Fully exponential Laplace approximations for the joint modelling of survival and longitudinal data.  _Journal of the Royal Statistical Society, Series B_ , 71:637–654, 2009.
  * Robinson and Smyth (2008) M. D. Robinson and G. K. Smyth.  Small-sample estimation of negative binomial dispersion, with applications to SAGE data.  _Biostatistics_ , 9:321–.332, 2008.
  * Rousseeuw and Christmann (2003) P. J. Rousseeuw and A. Christmann.  Robustness against separation and outliers in logistic regression.  _Computational Statistics and Data Analysis_ , 43:315–332, 2003.
  * Saha and Paul (2005) K. Saha and S. Paul.  Bias-corrected maximum likelihood estimator of the negative binomial dispersion parameter.  _Biometrics_ , 61:179–185, 2005.
  * Santner and Duffy (1986) T. J. Santner and D. E. Duffy.  A note on A. Albert and J. A. Anderson’s conditions for the existence of maximum likelihood estimates in logistic regression models.  _Biometrika_ , 73:755–758, 1986.
  * Sartori (2003) N. Sartori.  Modified profile likelihoods in models with stratum nuisance parameters.  _Biometrika_ , 90:533–549, 2003.
  * Schaefer (1983) R. L. Schaefer.  Bias correction in maximum likelihood logistic regression.  _Statistics in Medicine_ , 2:71–78, 1983.
  * Severini (1998) T. A. Severini.  An approximation to the modified profile likelihood function.  _Biometrika_ , 85:403–411, 1998.
  * Severini (2000) T. A. Severini.  _Likelihood methods in statistics_.  Oxford University Press, Oxford, 2000.
  * Severini (2002) T. A. Severini.  Modified estimating functions.  _Biometrika_ , 89:333–343, 2002.
  * Shah and Samworth (2013) R. D. Shah and R. J. Samworth.  Variable selection with error control: another look at stability selection.  _Journal of the Royal Statistical Society: Series B_ , 75:55–80, 2013.
  * Silvapulle (1981) M. J. Silvapulle.  On the existence of maximum likelihood estimators for the binomial response models.  _Journal of the Royal Statistical Society, Series B_ , 43:310–313, 1981.
  * Simas et al. (2011) A. B. Simas, A. V. Rocha, and W. Barreto-Souza.  Bias-corrected estimators for dispersion models with dispersion covariates.  _Journal of Statistical Planning and Inference_ , 141:3063–3074, 2011.
  * Smith (1993) A. A. Smith.  Estimating nonlinear time-series models using simulated vector autoregressions.  _Journal of Applied Econometrics_ , 8(S1):S63–S84, 1993.
  * Smith (2008) Jr. A. A. Smith.  Indirect inference.  In S. Durlauf and L. Blume, editors, _The New Palgrave Dictionary of Economics_. Palgrave Macmillan, London, 2nd edition, 2008.
  * Stefanski et al. (1986) L. A. Stefanski, R. J. Carroll, and D. Ruppert.  Optimally bounded score functions for generalized linear models with applicationto logistic regression.  _Biometrika_ , 73:413–424, 1986.
  * Steyerberg et al. (1999) E. W. Steyerberg, M. J. C. Eijkemans, and J. D. F. Habbema.  Stepwise selection in small data sets: A simulation study of bias in logistic regression analysis.  _Journal of Clinical Epidemiology_ , 52:935–942, 1999.
  * Sur and Candès (2018) P. Sur and E. J. Candès.  A modern maximum-likelihood theory for high-dimensional logistic regression.  Technical report, Stanford University, Stanford, CA 94305, USA, 2018.  Working paper available at: https: // arXiv:1803.06964v4.
  * Tabatabai et al. (2014) M. Tabatabai, H. Li, W. Eby, J. Kengwoung-Keumo, U. Manne, S. Bae, M. Fouad, and K. Singh.  Robust logistic and probit methods for binary and multinomial regression.  _Journal of Biometrics and Biostatistics_ , 5, 2014.
  * Tibshirani (1996) R. Tibshirani.  Regression shrinkage and selection via the lasso.  _JRSSB_ , 58:267–288, 1996.
  * Tierney et al. (1989) L. Tierney, R. Kass, and J. Kadane.  Fully exponential laplace approximations to expectations and variances of nonpositive functions.  _Journal of the American Statistical Association_ , 84:710–716, 1989.
  * Tikhonov (1943) A. N. Tikhonov.  On the stability of inverse problems.  _Comptes rendus (Doklady) de l’Academie des Sciences de l’URSS_ , 39:195–198, 1943.
  * van de Geer et al. (2014) S. van de Geer, P. Bühlmann, Y. Ritov, and R. Dezeure.  On asymptotically optimal confidence regions and tests for high-dimensional models.  _The Annals of Statistics_ , 42:1166–1202, 2014.
  * Venables and Ripley (2002) W. N. Venables and B. D. Ripley.  _Modern Applied Statistics with S_.  Springer, New York, fourth edition, 2002.  URL http://www.stats.ox.ac.uk/pub/MASS4.
  * Victoria-Feser (2002) M.-P. Victoria-Feser.  Robust inference with binary data.  _Psychometrika_ , 67:21–32, 2002.
  * Victoria-Feser and Ronchetti (1997) M.-P. Victoria-Feser and E. Ronchetti.  Robust estimation for grouped data.  _Journal of the American Statistical Association_ , 92:333–340, 1997.
  * Vittinghoff and McCulloch (2007) E. Vittinghoff and C. E. McCulloch.  Relaxing the rule of ten events per variable in logistic and cox regression.  _American Journal of Epidemiology_ , 165:710–718, 2007\.
  * Wang and Hanfelt (2008) M. Wang and J. J. Hanfelt.  Robust modified profile estimating function with application to the generalized estimating equation.  _Journal of Statistical Planning and Inference_ , 138:2029–2044, 2008.
  * Wang (2014) X. Wang.  Firth logistic regression for rare variant association tests.  _Frontiers in Genetics_ , 5:187–188, 2014.
  * Wasserman and Roeder (2009) L. Wasserman and K. Roeder.  High-dimensional variable selection.  _The Annals of Statistics_ , 37:2178–2201, 2009.
  * Windham (1995) M. P. Windham.  Robustifying model fitting.  _Journal of the Royal Statistical Society, Series B_ , 57:599–609, 1995.
  * Young and Smith (2005) G. Young and R. Smith.  _Negative binomial regression (2nd ed.)_.  Cambridge University Press, New York, 2005.
  * Zeng (2017) G. Zeng.  On the existence of maximum likelihood estimates for weighted logistic regression.  _Communications in Statistics - Theory and Methods_ , 46:11194–11203, 2017.
  * Zhang and Zhang (2014) C.-H. Zhang and S. S. Zhang.  Confidence intervals for low dimensional parameters in high dimensional linear models.  _Journal of the Royal Statistical Society: Series B_ , 76:217–242, 2014.
  * Zhang and Huang (2008) Cun-Hui Zhang and Jian Huang.  The sparsity and bias of the lasso selection in high-dimensional linear regression.  _The Annals of Statistics_ , 36:1567–1594, 2008.
  * Zhang and Cheng (2017) X. Zhang and G. Cheng.  Simultaneous inference for high-dimensional linear models.  _Journal of the American Statistical Association_ , 112:757–768, 2017.
  * Zhu and Joe (2009) R. Zhu and H. Joe.  Modelling heavy-tailed count data using a generalised Poisson-inverse Gaussian family.  _Statistics & Probability Letters_, 79:1695–1703, 2009\.