Limiting distributions of likelihood ratio test for independence of components for high-dimensional normal vectors

Yongcheng Qi (), Fang Wang () and Lin Zhang ()
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Yongcheng Qi: University of Minnesota Duluth
Fang Wang: Capital Normal University
Lin Zhang: University of Minnesota

Annals of the Institute of Statistical Mathematics, 2019, vol. 71, issue 4, No 8, 946 pages

Abstract: Abstract Consider a p-variate normal random vector. We are interested in the limiting distributions of likelihood ratio test (LRT) statistics for testing the independence of its grouped components based on a random sample of size n. In classical multivariate analysis, the dimension p is fixed or relatively small, and the limiting distribution of the LRT is a chi-square distribution. When p goes to infinity, the chi-square approximation to the classical LRT statistic may be invalid. In this paper, we prove that the LRT statistic converges to a normal distribution under quite general conditions when p goes to infinity. We propose an adjusted test statistic which has a chi-square limit in general. Our comparison study indicates that the adjusted test statistic outperforms among the three approximations in terms of sizes. We also report some numerical results to compare the performance of our approaches and other methods in the literature.

Keywords: Likelihood ratio test; Covariance matrix; Independence; High-dimensional normal vector; Central limit theorem; Chi-square approximation (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10463-018-0666-9

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