The Annals of Statistics

Tests for covariance matrix with fixed or divergent dimension

Rongmao Zhang, Liang Peng, and Ruodu Wang

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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.

Article information

Source
Ann. Statist. Volume 41, Number 4 (2013), 2075-2096.

Dates
First available in Project Euclid: 23 October 2013

Permanent link to this document
http://projecteuclid.org/euclid.aos/1382547513

Digital Object Identifier
doi:10.1214/13-AOS1136

Mathematical Reviews number (MathSciNet)
MR3127858

Zentralblatt MATH identifier
1277.62151

Subjects
Primary: 62F03: Hypothesis testing
Secondary: 62F40: Bootstrap, jackknife and other resampling methods

Keywords
Covariance matrix empirical likelihood tests high-dimensional data $\chi^{2}$-distribution

Citation

Zhang, Rongmao; Peng, Liang; Wang, Ruodu. Tests for covariance matrix with fixed or divergent dimension. Ann. Statist. 41 (2013), no. 4, 2075--2096. doi:10.1214/13-AOS1136. http://projecteuclid.org/euclid.aos/1382547513.


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Supplemental materials

  • Supplementary material: Supplement to “Tests for covariance matrix with fixed or divergent dimension”. This supplementary file contains detailed proofs of Lemmas 4.1–4.5 used in Section 4.