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Activity Number: 203 - Advances in Nonparametric Testing
Type: Contributed
Date/Time: Monday, August 8, 2022 : 2:00 PM to 3:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract #322795
Title: Power-Enhanced Simultaneous Test of High-Dimensional Mean Vectors and Covariance Matrices with Application to Gene-Set Testing
Author(s): Xiufan Yu* and Danning Li and Lingzhou Xue and Runze Li
Companies: University of Notre Dame and Northeast Normal University and Penn State University and National Institute of Statistical Sciences and Penn State University
Keywords: Dense alternatives; Fisher's combination; Power-enhanced tests; Power enhancement components; Sparse alternatives
Abstract:

Power-enhanced tests with high-dimensional data have received growing attention in theoretical and applied statistics in recent years. Existing tests possess their respective high-power regions, and we may lack prior knowledge about the alternatives when testing for a problem of interest in practice. There is a critical need of developing powerful testing procedures against more general alternatives. This paper studies the joint test of two-sample mean vectors and covariance matrices for high-dimensional data. We first expand the high-power region of high-dimensional mean tests or covariance tests to a wider alternative space and then combine their strengths together in the simultaneous test. We develop a new power-enhanced simultaneous test that is powerful to detect differences in either mean vectors or covariance matrices under either sparse or dense alternatives. We prove that the proposed testing procedures align with the power enhancement principles introduced by Fan et al. (2015) and achieve the accurate asymptotic size and consistent asymptotic power. We demonstrate the finite-sample performance using simulation studies and a real application to gene-set testing.


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