Report：A Distribution-Free Test of Independence Based on Mean Variance Index

Time： 3:30pm Nov.29,2017

Place：Room104,Building of Statistics of School

Report：Cui Hengjian

Abstract：This work is concerned with testing the independence between a categorical random variable Y and a continuous one X based on mean variance index. The mean variance index can be considered as the weighted average of Cramer-von Mises distances between the conditional distribution functions of X given each class of Y and the unconditional distribution function of X. The mean variance index is zero if and only if X and Y are independent. We propose a new mean variance test based on the mean variance index between X and Y and it enjoys several appealing merits. First, under the independence between X and Y, we derive an explicit form of the asymptotic null distribution, it provides us an efficient and fast way to compute the empirical p-value in practice. Second, no assumption on the distribution of two random variables is required andthe new test statistic is invariant under one-to-one transformations of the continuous random variable. Thus, the proposed test is distribution-free. Furthermore, this test is resistent to heavy-tailed distributions and extreme values in the data. In addition, the mean variance test is also applicable to test the independence between two continuous random variables by discretizing one variable. Monte Carlo simulations show that the new test has an outstanding finite-sample power performance even the continuous variable X is generated from a standard Cauchy distribution.