CONTIGUITY under HIGH-DIMENSIONAL GAUSSIANITY with APPLICATIONS to COVARIANCE TESTING

Qiyang Han, Tiefeng Jiang, Yandi Shen

Research output: Contribution to journalArticlepeer-review

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Abstract

Le Cam s third/contiguity lemma is a fundamental probabilistic tool to compute the limiting distribution of a given statistic Tn under a nonnull sequence of probability measures {Qn}, provided its limiting distribution under a null sequence {Pn} is available, and the log likelihood ratio {log(dQn/dPn)} has a distributional limit. Despite its wide-spread applications to low-dimensional statistical problems, the stringent requirement of Le Cam s third/contiguity lemma on the distributional limit of the log likelihood ratio makes it challenging, or even impossible to use in many modern highdimensional statistical problems.

Original languageEnglish (US)
Pages (from-to)4272-4321
Number of pages50
JournalAnnals of Applied Probability
Volume33
Issue number6A
DOIs
StatePublished - Dec 2023

Bibliographical note

Publisher Copyright:
© 2023 Institute of Mathematical Statistics. All rights reserved.

Keywords

  • Contiguity
  • covariance test
  • Poincaré inequalities.
  • power analysis

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