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On the optimization of the weighted Bickel-Rosenblatt test

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  • Chebana, Fateh
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 68 (2004)
    Issue (Month): 4 (July)
    Pages: 333-345

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    Handle: RePEc:eee:stapro:v:68:y:2004:i:4:p:333-345

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    Related research

    Keywords: Goodness-of-fit tests Kernel density estimator Weighted L2-norm Pitman's efficiency;

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    1. 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.
    2. repec:ese:iserwp:95-01 is not listed on IDEAS
    3. Carlos TENREIRO, 1996. "Tests d'ajustement à une densité fondés sur un estimateur non paramétrique à noyau pour des observations dépendantes," Annales d'Economie et de Statistique, ENSAE, issue 43, pages 129-148.
    4. Fan, Yanqin, 1994. "Testing the Goodness of Fit of a Parametric Density Function by Kernel Method," Econometric Theory, Cambridge University Press, vol. 10(02), pages 316-356, June.
    5. 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.
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