Tests for independence against regression and expectation dependence

Abstract

In this paper, we propose nonparametric tests based on U-statistics for testing independence against two different classes of alternatives: positive regression dependence and positive expectation dependence. We obtain the asymptotic distribution of the test statistics both under the null and the alternative hypothesis. An extensive Monte Carlo simulation study is done to assess the finite sample performance of the proposed tests. The test procedures are illustrated using two data sets.