Tests based on characterizations, and their efficiencies: a survey

  • Ya. Nikitin Department of Mathematics and Mechanics, Saint-Petersburg State University, Universitetskaia nab. 7/9, Saint-Petersburg 199034 / National Research University - Higher School of Economics, Souza Pechatnikov 16, Saint-Petersburg 190008
Keywords: Characterization of distribution, goodness-of-fit, symmetry, U-statistics, Bahadur efficiency


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.