Approximating the null distribution of a class of statistics for testing independence

Abstract

A class of tests for testing independence whose test statistic is an L 2 -norm of the difference between the joint empirical characteristic function and the product of the marginal empirical characteristic functions associated with a sample is considered. Since the null distribution of these test statistics is unknown, some approximations are investigated. Specifically, the permutation, bootstrap and weighted bootstrap estimators are examined. All of them provide consistent estimators. A simulation study analyzes the performance of these approximations for small and moderate sample sizes. An application to a real data set for testing independence between positional errors in spatial data is included.