Composite T22 test for high-dimensional data

Long Feng, Changliang Zou, Zhaojun Wang, Lixing ZHU

Research output: Contribution to journalArticlepeer-review

Abstract

We consider high-dimensional location test problems in which the number of variables p may exceed the sample size n. The classical T22 test does not work well because the contamination bias in estimating the covariance matrix grows rapidly with p. Unlike most existing remedies abandoning all the correlation information, the composite T22 test developed here makes use of them in a practical and efficient way. Under mild conditions, the proposed test statistic is asymptotically normal, and allows the dimensionality to almost exponentially increase in n. The test inherits certain appealing features of the classical T22 test and does not su er from large bias contamination. Due to incorporating much correlation information, the proposed test can deliver more robust performance than existing methods in many cases. Simulation studies demonstrate the validity of asymptotic analysis.

Original languageEnglish
Pages (from-to)1419-1436
Number of pages18
JournalStatistica Sinica
Volume27
Issue number3
DOIs
Publication statusPublished - Jul 2017

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Asymptotic normality
  • Composite T test
  • High-dimensional data
  • Large-p-small-n

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