## The power and optimal kernel of the Bickel-Rosenblatt test for goodness of fit.(English)Zbl 0741.62044

Summary: P. J. Bickel and M. Rosenblatt [ibid. 1, 1071-1095 (1973; Zbl 0275.62033), Correction ibid. 3, 1370 (1975)] proposed a procedure for testing 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 $$b_ n$$ and an arbitrary weight function $$\alpha$$. We study the behavior of the asymptotic power of the test and show that a uniform kernel maximizes the power when $$\alpha>0$$.

### MSC:

 62G10 Nonparametric hypothesis testing 62G20 Asymptotic properties of nonparametric inference

Zbl 0275.62033
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