Asymptotic theory for maximum deviations of sample covariance matrix estimates

Han Xiao, Wei Biao Wu

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


We consider asymptotic distributions of maximum deviations of sample covariance matrices, a fundamental problem in high-dimensional inference of covariances. Under mild dependence conditions on the entries of the data matrices, we establish the Gumbel convergence of the maximum deviations. Our result substantially generalizes earlier ones where the entries are assumed to be independent and identically distributed, and it provides a theoretical foundation for high-dimensional simultaneous inference of covariances.

Original languageEnglish (US)
Pages (from-to)2899-2920
Number of pages22
JournalStochastic Processes and their Applications
Issue number7
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


  • Covariance matrix
  • High dimensional analysis
  • Maximal deviation
  • Tapering
  • Test for bandedness
  • Test for covariance structure
  • Test for stationarity


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