Robust estimation of high-dimensional covariance and precision matrices

Marco Avella-Medina, Heather S. Battey, Jianqing Fan, Quefeng Li

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

High-dimensional data are often most plausibly generated from distributions with complex structure and leptokurtosis in some or all components. Covariance and precision matrices provide a useful summary of such structure, yet the performance of popular matrix estimators typically hinges upon a sub-Gaussianity assumption. This paper presents robust matrix estimators whose performance is guaranteed for a much richer class of distributions. The proposed estimators, under a bounded fourth moment assumption, achieve the same minimax convergence rates as do existing methods under a sub-Gaussianity assumption. Consistency of the proposed estimators is also established under the weak assumption of bounded 2+ϵ moments for ϵ∈ (0,2). The associated convergence rates depend on ϵ.

Original languageEnglish (US)
Pages (from-to)271-284
Number of pages14
JournalBiometrika
Volume105
Issue number2
DOIs
StatePublished - Jun 1 2018

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Keywords

  • Constrained l-minimization
  • Leptokurtosis
  • Minimax rate
  • Robustness
  • Thresholding

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