Asymptotic power of likelihood ratio tests for high dimensional data

2013/02/14 by Wang, Cheng, Cao, Longbing, Miao, Baiqi
#62H15 #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1302.3302

Abstract

This paper considers the asymptotic power of likelihood ratio test (LRT) for the identity test when the dimension p is large compared to the sample size n. The asymptotic distribution of LRT under alternatives is given and an explicit expression of the power is derived. A simulation study is carried out to compare LRT with other tests. All these studies show that LRT is a powerful test to detect eigenvalues around zero. Key words and phrases: Covariance matrix, High dimensional data, Identity test, Likelihood ratio test, Power

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