A general Monte Carlo method for multivariate goodness-of-fit testing applied to elliptical families

TL;DR

This paper introduces a versatile Monte Carlo-based method for multivariate goodness-of-fit testing, specifically applied to elliptical distributions, utilizing characteristic functions to develop consistent test statistics.

Contribution

It presents a novel, simple Monte Carlo approach for multivariate goodness-of-fit tests that leverages characteristic functions, with proven consistency and comparative simulation analysis.

Findings

The proposed test is consistent and has favorable limit properties.

Simulation results show competitive performance against existing methods.

The method is applicable to elliptical distribution families.

Abstract

A general and relatively simple method for construction of multivariate goodness-of-fit tests is introduced. The proposed test is applied to elliptical distributions. The method is based on a characterization of probability distributions via their characteristic function. The consistency and other limit properties of the new test statistics are studied. Also in a simulation study the proposed tests are compared with earlier as well as more recent competitors.