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Activity Number: 352 - Contributed Poster Presentations: Korean International Statistical Society
Type: Contributed
Date/Time: Tuesday, August 1, 2017 : 10:30 AM to 12:20 PM
Sponsor: Korean International Statistical Society
Abstract #322863
Title: Permutation Based Testing on Covariance Separability
Author(s): Seongoh Park* and Johan Lim and Xinlei Wang and Sanghan Lee
Companies: and Seoul National University and Southern Methodist University and Nathan Kline Institute for Psychiatric Research, Orangeburg, NY, USA
Keywords: Bonferroni test ; Covariance matrix ; Multiple multivariate data ; Separability ; Permutation test ; Nonnormal data
Abstract:

Separability is an attractive feature of covariance matrices or matrix variate data, which can improve and simplify many multivariate procedures. Due to its importance, testing separability has attracted much attention in the past. The procedures in the literature are based on the LRT under normal assumption and aim to find a good approximation to its null distribution. Here, we develop a new approach that is very different from existing ones. We propose to reformulate the null hypothesis (the separability of a covariance matrix of interest) into many sub-hypotheses (the separability of the sub-matrices of the covariance matrix), which are testable using a permutation-based procedure. We then combine the testing results of sub-hypotheses using the Bonferroni and two-stage additive procedures. Our permutation based procedures are inherently distribution free; thus it is robust to non-normality of the data. In addition, unlike the LRT, they are applicable to situations when the sample size is smaller than the number of unknown parameters in the covariance matrix. Our numerical study and data examples show these advantages of our procedures over the existing LRT.


Authors who are presenting talks have a * after their name.

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