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高维情形下基于距离与再生核希尔伯特空间的依赖度量AI 解读

In this paper, we study distance covariance, Hilbert–Schmidt covariance (aka Hilbert–Schmidt independence criterion [In Advances in Neural Information Processing Systems (2008) 585–592]) and related independence tests under the high dimensional scenario. We show that the sample distance/Hilbert–Schmidt covariance between two random vectors can be approximated by the sum of squared componentwise sample cross-covariances up to an asymptotically constant factor, which indicates…

基于距离协方差的高维相互独立性检验AI 解读

Summary We introduce an L2-type test for testing mutual independence and banded dependence structure for high dimensional data. The test is constructed on the basis of the pairwise distance covariance and it accounts for the non-linear and non-monotone dependences among the data, which cannot be fully captured by the existing tests based on either Pearson correlation or rank correlation. Our test can be conveniently implemented in practice as the limiting null distribution…

Motivated by applications in biological science, we propose a novel test to assess the conditional mean dependence of a response variable on a large number of covariates. Our procedure is built on the martingale difference divergence recently proposed in Shao and Zhang [J. Amer. Statist. Assoc. 109 (2014) 1302–1318], and it is able to detect certain type of departure from the null hypothesis of conditional mean independence without making any specific model assumptions.…