Limiting distributions of likelihood ratio test for independence of components for high-dimensional normal vectors
Limiting distributions of likelihood ratio test for independence of components for high-dimensional normal vectors
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DOI：
10.1007/s10463-018-0666-9
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发表时间：
2019-08
影响因子：
1
通讯作者：
Y. Qi;F. Wang;Lin Zhang
中科院分区：
文献类型：
--
作者：
Y. Qi;F. Wang;Lin Zhang
Consider ap-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 sizen. In classical multivariate analysis, the dimensionpis fixed or relatively small, and the limiting distribution of the LRT is a chi-square distribution. Whenpgoes 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 whenpgoes 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.
