1. Adaptive Sphericity Tests for High Dimensional Data
- Author
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Zhao, Ping, Yang, Wenwan, Feng, Long, and Wang, Zhaojun
- Subjects
Statistics - Methodology - Abstract
In this paper, we investigate sphericity testing in high-dimensional settings, where existing methods primarily rely on sum-type test procedures that often underperform under sparse alternatives. To address this limitation, we propose two max-type test procedures utilizing the sample covariance matrix and the sample spatial-sign covariance matrix, respectively. Furthermore, we introduce two Cauchy combination test procedures that integrate both sum-type and max-type tests, demonstrating their superiority across a wide range of sparsity levels in the alternative hypothesis. Our simulation studies corroborate these findings, highlighting the enhanced performance of our proposed methodologies in high-dimensional sphericity testi
- Published
- 2024