On characterization based goodness-of-fit tests: a review of recent results

Abstract

Recently, characterization based approach for the construction of goodness-of-fit tests has become rather popular. Such tests are attractive because they reflect some intrinsic properties of probability distributions connected with the given characterization, and therefore can be more efficient or more robust than others. The growth of the number of characterization theorems especially contributed to the development of this direction. In this talk, we present several types of characterization theorems as well as several approaches for the construction of goodness-of-fit tests. General approaches will be accompanied with particular examples of recently proposed tests for Exponential, Pareto, Uniform and Lévy distribution. The presentation will be based on the references given below, as well as some working results. In addition, some promising directions for future research will be given.