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On the optimization of the weighted Bickel-Rosenblatt test

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  • Chebana, Fateh

Abstract

We consider Bickel-Rosenblatt tests of fit for a density f. Their asymptotic properties are studied under Pitman's local alternatives; we investigate their power functions. Our goal is to look for the best test in this class, by optimizing the power as done by Mason (Ann. Statist. 11 (1983) 317) in the context of minimax comparisons. This approach leads to a continuous versions of a [chi]2 type test. Finally a simulation study is presented.

Suggested Citation

  • Chebana, Fateh, 2004. "On the optimization of the weighted Bickel-Rosenblatt test," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 333-345, July.
    • Handle: RePEc:eee:stapro:v:68:y:2004:i:4:p:333-345
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    References listed on IDEAS

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    1. Jenkins, Stephen P., 1995. "Did the middle class shrink during the 1980s? UK evidence from kernel density estimates," Economics Letters, Elsevier, vol. 49(4), pages 407-413, October.
    2. Fan, Yanqin, 1994. "Testing the Goodness of Fit of a Parametric Density Function by Kernel Method," Econometric Theory, Cambridge University Press, vol. 10(2), pages 316-356, June.
    3. repec:adr:anecst:y:1996:i:43:p:06 is not listed on IDEAS
    4. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
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