Empirical likelihood method for complete independence test on high-dimensional data

Yongcheng Qi, Yingchao Zhou

Research output: Contribution to journalArticlepeer-review

Abstract

Given a random sample of size n from a p dimensional random vector, we are interested in testing whether the p components of the random vector are mutually independent. This is the so-called complete independence test. In the multivariate normal case, it is equivalent to testing whether the correlation matrix is an identity matrix. In this paper, we propose a one-sided empirical likelihood method for the complete independence test based on squared sample correlation coefficients. The limiting distribution for our one-sided empirical likelihood test statistic is proved to be (Formula presented.) when both n and p tend to infinity, where Z is a standard normal random variable. In order to improve the power of the empirical likelihood test statistic, we also introduce a rescaled empirical likelihood test statistic. We carry out an extensive simulation study to compare the performance of the rescaled empirical likelihood method and two other statistics.

Original languageEnglish (US)
JournalJournal of Statistical Computation and Simulation
DOIs
StateAccepted/In press - 2022

Bibliographical note

Publisher Copyright:
© 2022 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

  • complete independence test
  • Empirical likelihood
  • high-dimension
  • multivariate normal distribution

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