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June 2019 Two-sample and ANOVA tests for high dimensional means
Song Xi Chen, Jun Li, Ping-Shou Zhong
Ann. Statist. 47(3): 1443-1474 (June 2019). DOI: 10.1214/18-AOS1720


This paper considers testing the equality of two high dimensional means. Two approaches are utilized to formulate $L_{2}$-type tests for better power performance when the two high dimensional mean vectors differ only in sparsely populated coordinates and the differences are faint. One is to conduct thresholding to remove the nonsignal bearing dimensions for variance reduction of the test statistics. The other is to transform the data via the precision matrix for signal enhancement. It is shown that the thresholding and data transformation lead to attractive detection boundaries for the tests. Furthermore, we demonstrate explicitly the effects of precision matrix estimation on the detection boundary for the test with thresholding and data transformation. Extension to multi-sample ANOVA tests is also investigated. Numerical studies are performed to confirm the theoretical findings and demonstrate the practical implementations.


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Song Xi Chen. Jun Li. Ping-Shou Zhong. "Two-sample and ANOVA tests for high dimensional means." Ann. Statist. 47 (3) 1443 - 1474, June 2019.


Received: 1 June 2016; Revised: 1 July 2017; Published: June 2019
First available in Project Euclid: 13 February 2019

zbMATH: 07053514
MathSciNet: MR3911118
Digital Object Identifier: 10.1214/18-AOS1720

Primary: 62H15
Secondary: 62E20

Keywords: ANOVA , data transformation , Large $p$ small $n$ , sparse signals , thresholding , two-sample tests for means

Rights: Copyright © 2019 Institute of Mathematical Statistics


Vol.47 • No. 3 • June 2019
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