Asymptotic theory for maximum deviations of sample covariance matrix estimates

Han Xiao and Wei Biao Wu

Stochastic Processes and their Applications, 2013, vol. 123, issue 7, 2899-2920

Abstract: 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.

Keywords: Covariance matrix; High dimensional analysis; Maximal deviation; Tapering; Test for bandedness; Test for covariance structure; Test for stationarity (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:7:p:2899-2920

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DOI: 10.1016/j.spa.2013.03.012

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