Asymptotic theory for maximum deviations of sample covariance matrix estimates. (English) Zbl 1284.62122

Xiao, Han; Wu, Wei Biao

Stochastic Processes Appl. 123, No. 7, 2899-2920 (2013).

Summary: 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 provides a theoretical foundation for high-dimensional simultaneous inference of covariances.

MSC:

62E20	Asymptotic distribution theory in statistics
62H10	Multivariate distribution of statistics
62H15	Hypothesis testing in multivariate analysis

Keywords:

high dimensional analysis; tapering; test for bandedness; test for covariance structure; test for stationarity

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