Two-Sample Tests for High Dimensional Means with Thresholding and Data Transformation

2014/10/10 by Song Xi Chen, Jun Li, Chen, Song Xi +3 · 2 citations
Mathematics · #FOS: Computer and information sciences #Methodology (stat.ME) #Random Matrices and Applications #Statistical Methods and Bayesian Inference #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1410.2848

openalex publication_date 2014/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider testing for two-sample means of high dimensional populations by thresholding. Two tests are investigated, which are designed for better power performance when the two population mean vectors differ only in sparsely populated coordinates. The first test is constructed by carrying out thresholding to remove the non-signal bearing dimensions. The second test combines data transformation via the precision matrix with the thresholding. The benefits of the thresholding and the data transformations are showed by a reduced variance of the test thresholding statistics, the improved power and a wider detection region of the tests. Simulation experiments and an empirical study are performed to confirm the theoretical findings and to demonstrate the practical implementations.

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