Asymptotic theory for maximum deviations of sample covariance matrix estimates

Han Xiao; Wei Biao Wu

doi:10.1016/j.spa.2013.03.012

Asymptotic theory for maximum deviations of sample covariance matrix estimates

Han Xiao, Wei Biao Wu

School of Arts and Sciences, Statistics

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

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.

Original language	English (US)
Pages (from-to)	2899-2920
Number of pages	22
Journal	Stochastic Processes and their Applications
Volume	123
Issue number	7
DOIs	https://doi.org/10.1016/j.spa.2013.03.012
State	Published - 2013

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modeling and Simulation
Applied Mathematics

Keywords

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

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10.1016/j.spa.2013.03.012

Cite this

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title = "Asymptotic theory for maximum deviations of sample covariance matrix estimates",

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",

author = "Han Xiao and Wu, {Wei Biao}",

note = "Funding Information: Han Xiao{\textquoteright}s research was supported in part by the US National Science Foundation ( DMS-1209091 ). Wei Biao Wu{\textquoteright}s research was supported in part by the US National Science Foundation ( DMS-0906073 and DMS-1106970 ). ",

year = "2013",

doi = "10.1016/j.spa.2013.03.012",

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T1 - Asymptotic theory for maximum deviations of sample covariance matrix estimates

AU - Xiao, Han

AU - Wu, Wei Biao

N1 - Funding Information: Han Xiao’s research was supported in part by the US National Science Foundation ( DMS-1209091 ). Wei Biao Wu’s research was supported in part by the US National Science Foundation ( DMS-0906073 and DMS-1106970 ).

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Covariance matrix

KW - High dimensional analysis

KW - Maximal deviation

KW - Tapering

KW - Test for bandedness

KW - Test for covariance structure

KW - Test for stationarity

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DO - 10.1016/j.spa.2013.03.012

M3 - Article

AN - SCOPUS:84885041889

SN - 0304-4149

VL - 123

SP - 2899

EP - 2920

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 7

ER -

Asymptotic theory for maximum deviations of sample covariance matrix estimates

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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