Asymptotic normality and moderate deviation principle for high-dimensional likelihood ratio statistic on block compound symmetry covariance structure. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Sun, Gaoming; Xie, Junshan
• Is Part Of: Statistics. Volume 54:Issue 1(2020)
• Page Start: 114
• Page End: 134
• Publication Date: 2020-01-02
• Subjects: Likelihood ratio test -- high-dimensional data -- BCS covariance structure -- asymptotic normality -- moderate deviation principle; Primary: 62H15 -- Secondary: 62E20 -- 60F05; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2020.1715408
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: The paper considers a high-dimensional likelihood ratio (LR) test on the block compound symmetric (BCS) covariance structure of a multivariate Gaussian population. When the dimension of each block p, the number of blocks u and the sample size n satisfy that p = p ( n ) → ∞ and pu < n −1 as n → ∞, the asymptotic normality and the moderate deviation principle of the logarithmic LR statistic are obtained. Some numerical simulations demonstrate that the proposed method in high-dimensional BCS test outperforms the traditional Chi-square approximation method, and it is as efficient as the Edgeworth expansion method by Mitsui et al. [Likelihood ratio test statistic for block compound symmetry covariance structure and its asymptoic expansion. Technical Report No.15-03, Statistical Research Group, Hiroshima University, Japan; 2015]. In addition, the proposed method is more applicable because the asymptotic distribution of the test statistic is more concise and the restriction on parameters p, u is milder.