Tests for covariance matrix with fixed or divergent dimension
Rongmao Zhang, Liang Peng, Ruodu Wang
The Annals of Statistics · 2013 · Volume 41 · Issue 4
Abstract
Testing covariance structure is of importance in many areas of statistical analysis, such as microarray analysis and signal processing. Conventional tests for finite-dimensional covariance cannot be applied to high-dimensional data in general, and tests for high-dimensional covariance in the literature usually depend on some special structure of the matrix. In this paper, we propose some empirical likelihood ratio tests for testing whether a covariance matrix equals a given one or has a banded structure. The asymptotic distributions of the new tests are independent of the dimension.
Keywords
$\chi^{2}$-distribution, 62F03, 62F40, Covariance matrix, empirical likelihood tests, High-dimensional data
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