On automatic kernel density estimate-based tests for goodness-of-fit

Although estimation and testing are different statistical problems, if we want to use a test statistic based on the Parzen–Rosenblatt estimator hypothesis that underlying density function f is member of location-scale family probability functions, it may be found reasonable choose smoothing parameter in such way kernel an effective irrespective which null or alternative true. In this paper address question by considering well-known Bickel–Rosenblatt statistics quadratic distance between nonparametric two parametric estimators under hypothesis. For each one these describe their asymptotic behaviours for general data-dependent parameter, state limiting Gaussian distribution consistency associated goodness-of-fit procedures families. order compare finite sample power performance tests hypothesis-based bandwidth selector with other methods existing literature, simulation study normal, logistic Gumbel models included work.