TESTS FOR COVARIANCE STRUCTURES WITH HIGH-DIMENSIONAL REPEATED MEASUREMENTS

• 成果类型: Article
• 署名作者: Zhong, Ping-Shou; Lan, Wei; Song, Peter X. K.; Tsai, Chih-Ling
• 署名单位: Michigan State University; University of Michigan System; University of Michigan; University of California System; University of California Davis
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/16-AOS1481
• 发表日期: 2017
• 页码: 1185-1213
• 关键词: sphericity; matrix

摘要

In regression analysis with repeated measurements, such as longitudinal data and panel data, structured covariance matrices characterized by a small number of parameters have been widely used and play an important role in parameter estimation and statistical inference. To assess the adequacy of a specified covariance structure, one often adopts the classical likelihood-ratio test when the dimension of the repeated measurements (p) is smaller than the sample size (n). However, this assessment becomes quite challenging when p is bigger than n, since the classical likelihood-ratio test is no longer applicable. This paper proposes an adjusted goodness-of-fit test to examine a broad range of covariance structures under the scenario of large p, small n. Analytical examples are presented to illustrate the effectiveness of the adjustment. In addition, large sample properties of the proposed test are established. Moreover, simulation studies and a real data example are provided to demonstrate the finite sample performance and the practical utility of the test.