Goodness-of-fit tests for multivariate skewed distributions based on the characteristic function

TL;DR

This paper introduces a Monte Carlo-based goodness-of-fit testing method for multivariate skewed distributions using characteristic functions, which is practical and effective for models with asymmetry and heavy tails.

Contribution

It proposes a novel weighted L2-type test based on empirical characteristic functions that does not require explicit population quantities, suitable for complex skewed distributions.

Findings

Test performs well in finite samples across various skewed distributions

Method effectively handles heavy tails and asymmetry in multivariate models

Real-data examples demonstrate practical applicability

Abstract

We employ a general Monte Carlo method to test composite hypotheses of goodness-of-fit for several popular multivariate models that can accommodate both asymmetry and heavy tails. Specifically, we consider weighted L2-type tests based on a discrepancy measure involving the distance between empirical characteristic functions and thus avoid the need for employing corresponding population quantities which may be unknown or complicated to work with. The only requirements of our tests are that we should be able to draw samples from the distribution under test and possess a reasonable method of estimation of the unknown distributional parameters. Monte Carlo studies are conducted to investigate the performance of the test criteria in finite samples for several families of skewed distributions. Real-data examples are also included to illustrate our method.