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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

Abstract

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.

Citation

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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. https://doi.org/10.1214/19-AOS1869

Information

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

Subjects:
Primary: 62J99
Secondary: 60B20

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 3 • June 2020
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