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June, 1991 The Power and Optimal Kernel of the Bickel-Rosenblatt Test for Goodness of Fit
B. K. Ghosh, Wei-Min Huang
Ann. Statist. 19(2): 999-1009 (June, 1991). DOI: 10.1214/aos/1176348133

Abstract

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 $b_n$ 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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B. K. Ghosh. Wei-Min Huang. "The Power and Optimal Kernel of the Bickel-Rosenblatt Test for Goodness of Fit." Ann. Statist. 19 (2) 999 - 1009, June, 1991. https://doi.org/10.1214/aos/1176348133

Information

Published: June, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0741.62044
MathSciNet: MR1105857
Digital Object Identifier: 10.1214/aos/1176348133

Subjects:
Primary: 62G10
Secondary: 62G20

Rights: Copyright © 1991 Institute of Mathematical Statistics

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Vol.19 • No. 2 • June, 1991
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