Covariance matrix testing in high dimension using random projections

Deepak Nag Ayyala, Santu Ghosh, Daniel F. Linder

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Estimation and hypothesis tests for the covariance matrix in high dimensions is a challenging problem as the traditional multivariate asymptotic theory is no longer valid. When the dimension is larger than or increasing with the sample size, standard likelihood based tests for the covariance matrix have poor performance. Existing high dimensional tests are either computationally expensive or have very weak control of type I error. In this paper, we propose a test procedure, CRAMP (covariance testing using random matrix projections), for testing hypotheses involving one or more covariance matrices using random projections. Projecting the high dimensional data randomly into lower dimensional subspaces alleviates of the curse of dimensionality, allowing for the use of traditional multivariate tests. An extensive simulation study is performed to compare CRAMP against asymptotics-based high dimensional test procedures. An application of the proposed method to two gene expression data sets is presented.

Original languageEnglish (US)
Pages (from-to)1111-1141
Number of pages31
JournalComputational Statistics
Issue number3
StatePublished - Jul 2022


  • Covariance matrix
  • High dimension
  • Hypothesis testing
  • Random projections

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Mathematics


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