Tests based on characterizations, and their efficiencies: a survey

Abstract

A survey of goodness-of-fit and symmetry tests based on the characterization properties of distributions is presented. This approach became popular in recent years. In most cases the test statistics are functionals of $U$-empirical processes. The limiting distributions and large deviations of new statistics under the null hypothesis are described. Their local Bahadur efficiency for various parametric alternatives is calculated and compared with each other as well as with diverse previously known tests. We also describe new directions of possible research in this domain.

Open access in Acta et Commentationes Universitatis Tartuensis de Mathematica

References in corpus (2)

• Two-dimensional Kolmogorov-type Goodness-of-fit Tests Based on Characterizations and their Asymptotic Efficiencies
• On two simple tests for normality with high power

Cited by in corpus (4)

• Fixed point characterizations of continuous univariate probability distributions and their applications
• Characterizations of non-normalized discrete probability distributions and their application in statistics
• New consistent exponentiality tests based on $V$-empirical Laplace transforms with comparison of efficiencies
• A new omnibus test of fit based on a characterisation of the uniform distribution