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The Bahadur risk in probability density estimation

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  • Korostelev Alexander

Abstract

A nonparametric probability density estimation problem is studied for the Bahadur-type risk under the sup-norm losses. The risk is minimax over the Hölder classes of densities. The large sample limiting performance of this risk is found, and the links to asymptotic equivalent white-noise models are discussed.

Suggested Citation

  • Korostelev Alexander, 2003. "The Bahadur risk in probability density estimation," Statistics & Risk Modeling, De Gruyter, vol. 21(2), pages 139-148, February.
    • Handle: RePEc:bpj:strimo:v:21:y:2003:i:2/2003:p:139-148:n:3
    DOI: 10.1524/stnd.21.2.139.19002
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    References listed on IDEAS

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    1. Korostelev A. & Leonov S., 1998. "Bahadur-Type Risks And Optimal Designs In Regression Problems," Statistics & Risk Modeling, De Gruyter, vol. 16(4), pages 333-348, April.
    2. Djamal Louani, 1998. "Large Deviations Limit Theorems for the Kernel Density Estimator," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 243-253, March.
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