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Multivariate goodness-of-fit tests based on kernel density estimators. (English) Zbl 1420.62156

Summary: 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.

MSC:

62G07 Density estimation
62H15 Hypothesis testing in multivariate analysis
62E20 Asymptotic distribution theory in statistics

Software:

KernSmooth; pyuvdata
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Full Text: DOI

References:

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