Testing the order of a population spectral distribution for high-dimensional data

Yingli Qin and Weiming Li

Computational Statistics & Data Analysis, 2016, vol. 95, issue C, 75-82

Abstract: Large covariance matrices play a fundamental role in various high-dimensional statistics. Investigating the limiting behavior of the eigenvalues can reveal informative structures of large covariance matrices, which is particularly important in high-dimensional principal component analysis and covariance matrix estimation. In this paper, we propose a framework to test the number of distinct population eigenvalues for large covariance matrices, i.e. the order of a Population Spectral Distribution. The limiting distribution of our test statistic for a Population Spectral Distribution of order 2 is developed along with its (N,p) consistency, which is clearly demonstrated in our simulation study. We also apply our test to two classical microarray datasets.

Keywords: Covariance matrix; High-dimension; Hypothesis testing; Population spectral distribution (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:95:y:2016:i:c:p:75-82

DOI: 10.1016/j.csda.2015.09.009

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