Abstract

Ahmad et al. (in press) presented test statistics for sphericity and identity of the covariance matrix of a multivariate normal distribution when the dimension, p, exceeds the sample size, n. In this note, we show that their statistics are robust to normality assumption, when normality is replaced with certain mild assumptions on the traces of the covariance matrix. Under such assumptions, the test statistics are shown to follow the same asymptotic normal distribution as under normality for large p, also whenp >> n. The asymptotic normality is proved using the theory of U-statistics, and is based on very general conditions, particularly avoiding any relationship between n and p.

Keywords

Non normality; High dimensionality; Sphericity

Published in

Communications in Statistics - Theory and Methods
2015, Volume: 44, number: 7, pages: 1387-1398

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

Probability Theory and Statistics


Publication identifier

DOI: https://doi.org/10.1080/03610926.2013.770533

Permanent link to this page (URI)

https://res.slu.se/id/publ/73449