Weighted Statistic in Detecting Faint and Sparse Alternatives for High-Dimensional Covariance Matrices
Date of Issue2017
School of Physical and Mathematical Sciences
This article considers testing equality of two population covariance matrices when the data dimension p diverges with the sample size n (p/n → c > 0). We propose a weighted test statistic that is data-driven and powerful in both faint alternatives (many small disturbances) and sparse alternatives (several large disturbances). Its asymptotic null distribution is derived by large random matrix theory without assuming the existence of a limiting cumulative distribution function of the population covariance matrix. The simulation results confirm that our statistic is powerful against all alternatives, while other tests given in the literature fail in at least one situation. Supplementary materials for this article are available online.
Empirical spectral distribution
Journal of the American Statistical Association
© 2017 American Statistical Association. This is the author created version of a work that has been peer reviewed and accepted for publication in Journal of the American Statistical Association, published by Taylor & Francis on behalf of American Statistical Association. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1080/01621459.2015.1122602].