Open Access
June 2017 Tests for covariance structures with high-dimensional repeated measurements
Ping-Shou Zhong, Wei Lan, Peter X. K. Song, Chih-Ling Tsai
Ann. Statist. 45(3): 1185-1213 (June 2017). DOI: 10.1214/16-AOS1481


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this assessment becomes quite challenging when $p$ is bigger than $n$, since the classical likelihood-ratio test is no longer applicable.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.


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Ping-Shou Zhong. Wei Lan. Peter X. K. Song. Chih-Ling Tsai. "Tests for covariance structures with high-dimensional repeated measurements." Ann. Statist. 45 (3) 1185 - 1213, June 2017.


Received: 1 May 2015; Revised: 1 March 2016; Published: June 2017
First available in Project Euclid: 13 June 2017

zbMATH: 1368.62153
MathSciNet: MR3662452
Digital Object Identifier: 10.1214/16-AOS1481

Primary: 62H15
Secondary: 62G10 , 62G20

Keywords: Adjusted test , Goodness-of-fit test , longitudinal data , panel data

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.45 • No. 3 • June 2017
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