Tests for covariance structures with high-dimensional repeated measurements
Ping-Shou Zhong, Wei Lan, Peter X. K. Song, Chih-Ling Tsai
The Annals of Statistics · 2017 · Volume 45 · Issue 3
Abstract
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this assessment becomes quite challenging when $p$ is bigger than $n$, since the classical likelihood-ratio test is no longer applicable.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.
Keywords
62G10, 62G20, 62H15, Adjusted test, Goodness-of-fit test, longitudinal data, panel data
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