text: abstract: in this paper we introduce a novel approach for an important
  problem of break detection. specifically, we are interested in detection of
  an abrupt change in the covariance structure of a high-dimensional random
  process – a problem, which has applications in many areas e.g., neuroimaging and finance. the developed approach is essentially a testing procedure
  involving a choice of a critical level. to that end a non-standard bootstrap
  scheme is proposed and theoretically justified under mild assumptions. theoretical study features a result providing guaranties for break detection. all
  the theoretical results are established in a high-dimensional setting (dimensionality p  n). multiscale nature of the approach allows for a trade-off
  between sensitivity of break detection and localization. the approach can
  be naturally employed in an on-line setting. simulation study demonstrates
  that the approach matches the nominal level of false alarm probability and
  exhibits high power, outperforming a recent approach.
  msc 2010 subject classifications: primary 62m10, 62h15; secondary
  91b84, 62p10.
  keywords and phrases: multiscale, bootstrap, structural change, critical
  value, precision matrix.