Asymptotic theory for maximum deviations of sample covariance matrix estimates |
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Authors: | Han Xiao Wei Biao Wu |
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Institution: | 1. Department of Statistics and Biostatistics, Rutgers University, 501 Hill Center, 110 Frelinghuysen Road, Piscataway, NJ 08854, United States;2. Department of Statistics, The University of Chicago, 5734 S. University Ave, Chicago, IL 60637, United States |
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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. |
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Keywords: | primary 62H15 62H10 secondary 62E20 |
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