Nonparametric Monte Carlo tests for multivariate distributions

Abstract

In this paper, nonparametric Monte Carlo test procedures are proposed for composite hypotheses in which the multivariate distribution belongs to a nonparametric family. When a random variable is, in distribution, equal to a product of two independent variables, Monte Carlo simulations can be performed conditionally on one of the variables. They can be applied to testing several commonly used distributions including elliptically symmetric, reflectively symmetric, Liouville–Dirichlet and symmetric scale mixture distributions. The tests are exactly valid when the hypothetical distributions are without nuisance location parameters. Finite sample simulations show that the Monte Carlo tests outperform bootstrap tests. The method is illustrated with analysis of a real dataset.