1. Distribution-free tests of independence in high dimensions
- Author
-
Han Liu, Shizhe Chen, and Fang Han
- Subjects
Statistics and Probability ,Distribution free ,Multivariate random variable ,Statistics & Probability ,General Mathematics ,Kendall tau rank correlation coefficient ,Linear rank statistic ,Mathematics - Statistics Theory ,Mutual independence ,01 natural sciences ,010104 statistics & probability ,Gumbel distribution ,Kendall’s tau ,Spearman’s rho ,Econometrics ,0101 mathematics ,Independence (probability theory) ,Statistical hypothesis testing ,Mathematics ,Discrete mathematics ,Numerical and Computational Mathematics ,Rank-type U-statistic ,Applied Mathematics ,Statistics ,010102 general mathematics ,Articles ,Agricultural and Biological Sciences (miscellaneous) ,Statistics, Probability and Uncertainty ,General Agricultural and Biological Sciences ,Null hypothesis ,Type I and type II errors - Abstract
We consider the testing of mutual independence among all entries in a $d$-dimensional random vector based on $n$ independent observations. We study two families of distribution-free test statistics, which include Kendall's tau and Spearman's rho as important examples. We show that under the null hypothesis the test statistics of these two families converge weakly to Gumbel distributions, and propose tests that control the type I error in the high-dimensional setting where $d>n$. We further show that the two tests are rate-optimal in terms of power against sparse alternatives, and outperform competitors in simulations, especially when $d$ is large., Comment: to appear in Biometrika
- Published
- 2017