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On testing for an identity covariance matrix when the dimensionality equals or exceeds the sample size

Authors
Journal
Journal of Statistical Planning and Inference
0378-3758
Publisher
Elsevier
Publication Date
Volume
142
Issue
1
Identifiers
DOI: 10.1016/j.jspi.2011.07.019
Keywords
  • Covariance Matrix
  • High-Dimensional Data Analysis
  • Hypothesis Testing
  • Identity Matrix

Abstract

Abstract This article explores the problem of testing the hypothesis that the covariance matrix is an identity matrix when the dimensionality is equal to the sample size or larger. Two new test statistics are proposed under comparable assumptions to those statistics in the literature. The asymptotic distribution of the proposed test statistics are found and are shown to be consistent in the general asymptotic framework. An extensive simulation study shows the newly proposed tests are comparable to, and in some cases more powerful than, the tests for an identity covariance matrix currently in the literature.

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