Abstract

Test statistics for sphericity and identity of the covariance matrix are presented, when the data are multivariate normal and the dimension, p, can exceed the sample size, n. Under certain mild conditions mainly on the traces of the unknown covariance matrix, and using the asymptotic theory of U-statistics, the test statistics are shown to follow an approximate normal distribution for large p, also when p >> n. The accuracy of the statistics is shown through simulation results, particularly emphasizing the case when p can be much larger than n. A real data set is used to illustrate the application of the proposed test statistics.

Keywords

covariance testing; U-statistics; high-dimensional data; sphericity

Published in

Journal of Statistical Computation and Simulation
2015, Volume: 85, number: 13, pages: 2619-2631
Publisher: TAYLOR & FRANCIS LTD

SLU Authors

• Ahmad, Rauf

  • Department of Energy and Technology, Swedish University of Agricultural Sciences
    
  • Uppsala University

• von Rosen, Dietrich

  • Department of Energy and Technology, Swedish University of Agricultural Sciences
    
  • Linköping University

UKÄ Subject classification

Computational Mathematics


Publication identifier

DOI: https://doi.org/10.1080/00949655.2014.948441

Permanent link to this page (URI)

https://res.slu.se/id/publ/75523