Two-sample high dimensional mean test based on prepivots

Santu Ghosh, Deepak Nag Ayyala, Rafael Hellebuyck

Research output: Contribution to journalArticlepeer-review

Abstract

Testing equality of mean vectors is a very commonly used criterion when comparing two multivariate random variables. Traditional tests such as Hotelling's T2 become either unusable or output small power when the number of variables is greater than the combined sample size. A novel method is proposed using both prepivoting and Edgeworth expansion for testing the equality of two population mean vectors in a “large p, small n” setting. The asymptotic null distribution of the test statistic is derived and it is shown that the power of suggested test converges to one under certain alternatives when both n and p increase to infinity. Finite sample performance of the proposed test statistic is compared with other recently developed tests designed to also handle the “large p, small n” situation through simulations. The proposed test achieves competitive rates for both type I error rate and power. The usefulness of suggested test is illustrated by applications to two microarray gene expression data sets.

Original languageEnglish (US)
Article number107284
JournalComputational Statistics and Data Analysis
Volume163
DOIs
StatePublished - Nov 2021

Keywords

  • Dense and sparse alternatives
  • Edgeworth expansion
  • High dimensional
  • Mean vector test
  • Prepivoting

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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