Testing diagonality of high-dimensional covariance matrix under non-normality

作者：Xu, Kai^*

来源：Journal of Statistical Computation and Simulation, 2017, 87(16): 3208-3224.

DOI：10.1080/00949655.2017.1362405

• Diagonality test
• high-dimensional data
• multivariate analysis

Under non-normality, this article is concerned with testing diagonality of high-dimensional covariance matrix, which is more practical than testing sphericity and identity in high-dimensional setting. The existing testing procedure for diagonality is not robust against either the data dimension or the data distribution, producing tests with distorted type I error rates much larger than nominal levels. This is mainly due to bias from estimating some functions of high-dimensional covariance matrix under non-normality. Compared to the sphericity and identity hypotheses, the asymptotic property of the diagonality hypothesis would be more involved and we should be more careful to deal with bias. We develop a correction that makes the existing test statistic robust against both the data dimension and the data distribution. We show that the proposed test statistic is asymptotically normal without the normality assumption and without specifying an explicit relationship between the dimension p and the sample size n. Simulations show that it has good size and power for a wide range of settings.

• 出版日期2017
• 单位上海财经大学