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Activity Number: 201
Type: Contributed
Date/Time: Monday, August 1, 2016 : 10:30 AM to 11:15 AM
Sponsor: Section on Nonparametric Statistics
Abstract #321572
Title: Testing the Sphericity of a Covariance Matrix When the Dimension Is Much Larger Than the Sample Size
Author(s): Zeng Li*
Companies: The University of Hong Kong
Keywords: sphericity test ; ultra-large dimension ; John's test ; Quasi-likelihood ratio test

This paper focuses on the prominent sphericity test when the dimension p is much lager than sample size n. The classical likelihood ratio test(LRT) is no longer applicable when p>>n. Therefore a Quasi-LRT is proposed and its asymptotic distribution of the test statistic under the null when p/n goes to infinity is well established in this paper. We also re-examine the well-known John's invariant test for sphericity in this ultra-dimensional setting. An amazing result from the paper states that John's test statistic has exactly the same limiting distribution under the ultra-dimensional setting with under other high-dimensional settings known in the literature. Therefore, John's test has been found to possess the powerful dimension-proof property, which keeps exactly the same limiting distribution under the null with any (n,p)-asymptotic, i.e. 0< p/n< infinity, n goes to infinity. All asymptotic results are derived for general population with finite fourth order moment. Numerical experiments are implemented for comparison.

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

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