C. Tenreiro
Although estimation and testing are different statistical problems, if we want to use a test statistic based on the Parzen-Rosenblatt estimator to test the hypothesis that the underlying density function $f$ is a member of a location-scale family of probability density functions, it may be found reasonable to choose the smoothing parameter in such a way that the kernel density estimator is an effective estimator of $f$ irrespective of which of the null or the alternative hypothesis is true. In this work we address this question by considering the well-known Bickel-Rosenblatt test statistics which are based on the quadratic distance between the nonparametric kernel estimator and two parametric estimators of $f$ under the null hypothesis.
Keywords: Kernel density estimator; Goodness-of-fit tests; Bickel-Rosenblatt tests; Bandwidth selection.
Scheduled
Invited Session Recent advances in goodness-of-fit and k-sample tests
June 10, 2022 10:10 AM
A13
