The paper is devoted to goodness of fit tests based on probability density estimates generated by kernel functions. The test statistic is considered in the form of maximum of the normalized deviation of the estimate from its expected value or a hypothesized distribution density function. A comparative Monte Carlo power study of the investigated criterion is provided. Simulation results show that the proposed test is a powerful competitor to the existing 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 close to Gaussian random processes and fields introduced by Rudzkis ( , 2012.
The paper is devoted to multivariate goodness-of-fit ests based on kernel density estimators. Both simple and composite null hypotheses are investigated. The test statistic is considered in the form of maximum of the normalized deviation of the estimate from its expected value. The produced comparative Monte Carlo power study shows that the proposed test is a powerful competitor to the existing classical criteria for testing goodness of fit against a specific type of an alternative hypothesis. An analytical way to establish the asymptotic distribution of the test statistic is discussed, using the approximation results for the probabilities of high excursions of differentiable Gaussian random fields.
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