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Activity Number: 163 - Biometrics Section Byar Award Student Paper Session II
Type: Topic Contributed
Date/Time: Tuesday, August 4, 2020 : 10:00 AM to 11:50 AM
Sponsor: Biometrics Section
Abstract #312474
Title: Asymptotically Independent U-Statistics in High-Dimensional Testing
Author(s): Yinqiu He* and Gongjun Xu and Chong Wu and Wei Pan
Companies: University of Michigan and University of Michigan and Florida State University and University of Minnesota
Keywords: High-dimensional hypothesis test; U-statistics; Adaptive testing

Many high-dimensional hypothesis tests aim to globally examine marginal or low-dimensional features of a high-dimensional joint distribution, such as testing of mean vectors, covariance matrices and regression coefficients. This paper constructs a family of U-statistics as unbiased estimators of the lp-norms of those features. We show that under the null hypothesis, the U-statistics of different finite orders are asymptotically independent and normally distributed. Moreover, they are also asymptotically independent with the maximum-type test statistic, whose limiting distribution is an extreme value distribution. Based on the asymptotic independence property, we propose an adaptive testing procedure which combines p-values computed from the U-statistics of different orders. We further establish power analysis results and show that the proposed adaptive procedure maintains high power against various alternatives.

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

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