Open Access
June 2020 An adaptable generalization of Hotelling’s $T^{2}$ test in high dimension
Haoran Li, Alexander Aue, Debashis Paul, Jie Peng, Pei Wang
Ann. Statist. 48(3): 1815-1847 (June 2020). DOI: 10.1214/19-AOS1869


We propose a two-sample test for detecting the difference between mean vectors in a high-dimensional regime based on a ridge-regularized Hotelling’s $T^{2}$. To choose the regularization parameter, a method is derived that aims at maximizing power within a class of local alternatives. We also propose a composite test that combines the optimal tests corresponding to a specific collection of local alternatives. Weak convergence of the stochastic process corresponding to the ridge-regularized Hotelling’s $T^{2}$ is established and used to derive the cut-off values of the proposed test. Large sample properties are verified for a class of sub-Gaussian distributions. Through an extensive simulation study, the composite test is shown to compare favorably against a host of existing two-sample test procedures in a wide range of settings. The performance of the proposed test procedures is illustrated through an application to a breast cancer data set where the goal is to detect the pathways with different DNA copy number alterations across breast cancer subtypes.


Download Citation

Haoran Li. Alexander Aue. Debashis Paul. Jie Peng. Pei Wang. "An adaptable generalization of Hotelling’s $T^{2}$ test in high dimension." Ann. Statist. 48 (3) 1815 - 1847, June 2020.


Received: 1 May 2018; Revised: 1 January 2019; Published: June 2020
First available in Project Euclid: 17 July 2020

zbMATH: 07241613
MathSciNet: MR4124345
Digital Object Identifier: 10.1214/19-AOS1869

Primary: 62J99
Secondary: 60B20

Keywords: asymptotic property , Covariance matrix , Hotelling’s $T^{2}$ statistic , Hypothesis testing , locally most powerful tests , Random matrix theory

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 3 • June 2020
Back to Top