Bickel and Rosenblatt proposed a procedure for testing the goodness of fit of a specified density to observed data. The test statistic is based on the distance between the kernel density estimate and the hypothesized density, and it depends on a kernel K, a bandwidth bₙ and an arbitrary weight function a. We study the behavior of the asymptotic power of the test and show that a uniform kernel maximizes the power when $a > 0$.
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Ghosh et al. (1991) studied this question.
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