Goodness of fit tests based on kernel density estimators

Abstract

The paper is devoted to goodness of fit tests based on kernel estimators of probability density functions. In particular, univariate case is investigated. The test statistic is considered in the form of maximum of the normalized deviation of the estimate from its expected value. Produced comparative Monte Carlo power study show that the proposed test is a powerful competitor to the exist- ing classical criteria testing goodness of fit against a specific type of alternative hypothesis. An analytical way for establishing the asymptotic distribution of the test statistic is proposed, using the theory of high excursions of Gaussian random processes and fields introduced by Rudzkis [17,18]. The extension of the proposed methods to the multivariate case are discussed.