A1317
Title: A bootstrap two sample test for high-dimensional covariance matrices
Authors: Nilanjan Chakraborty - Missouri University of Science and Technology (United States) [presenting]
Sayar Karmakar - University of Florida (United States)
Hira Koul - Michigan State University (United States)
Abstract: A test for equality of two high-dimensional covariance matrices in the two-sample setting is introduced. The test is based on the maximum of absolute differences between entries of multiplier bootstrap Jackknifed estimators of the two sample covariance matrices. An extension of the central limit theorem for one-sample non-degenerate U statistics to two-sample non-degenerate U statistics is developed and used to derive asymptotic guarantees for level and power of the proposed test statistic under the null and local alternative hypotheses. Results are obtained under weak conditions on the moments of random vectors and tails of marginal distributions. Correlation structures of random vectors can be arbitrary, sample sizes need not be equal, and multivariate dimension is allowed to grow exponentially with sample sizes. The test is shown to be consistent against a class of shrinking nonparametric alternatives. Finite sample simulation studies and real-life datasets corroborate the theoretical findings.
