Nonparametric tests for tail monotonicity

Abstract

This article proposes nonparametric tests for tail monotonicity of bivariate random vectors. The test statistic is based on a Kolmogorov-Smirnov-type functional of the empirical copula. Depending on the serial dependence features of the data, we propose two multiplier bootstrap techniques to approximate the critical values. We show that the test is able to detect local alternatives converging to the null hypothesis at rate n^-1/2 with a non-trivial power. A simulation study is performed to investigate the finite-sample performance and finally the procedure is illustrated by testing intergenerational income mobility.