A Bayesian approach to nonparametric test problems
We propose an alternative approach to the classical ``nonparametric'' test problems, such as the goodness of fit test and the two-sample nonparametric test. In this approach, those problems are reviewed from the viewpoint of the estimation of the underlying population distributions and are formulated as the problem of model selection between Bayesian models. The model selection can be easily realized by choosing a model with the smallest ABIC, Akaike Bayesian information criterion. The approach provides the estimates of the density of the underlying population distribution(s) of any shape as well as the evaluation of the goodness of fit or the check of homogeneity of distributions.
scientific article; zbMATH DE number 4102301