A note on goodness of fit test using moments

Abstract

The purpose of this article is to introduce a general moment-based approach to derive formal goodness of fit tests of a parametric family. We show that, in general, an approximate normal test or a chi-squared test can be derived by exploring the moment structure of a parametric family, when moments up to certain order exist. The idea is simple and the resulting tests are easy to implement. To illustrate the use of this approach, we derive moment-based goodness of fit tests for some common discrete and continuous parametric families. We also compare the proposed tests with the well known Pearson-Fisher chi-square test and some distance tests in a simulation study.