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Remark concerning data-dependent bandwidth choice in density estimation

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  • Mielniczuk, Jan

Abstract

We treat the problem of a data-dependent bandwidth choice for kernel estimation of a density. The difference between the kernel estimate using MSE-optimal bandwidth h0 and its counterpart incorporating natural adaptive estimate is shown to be of order OP(n). This extends Krieger and Pickands (1981) result in the case of univariate density. An analogous theorem is also proved when the integrated mean square error is considered as a measure of performance.

Suggested Citation

  • Mielniczuk, Jan, 1990. "Remark concerning data-dependent bandwidth choice in density estimation," Statistics & Probability Letters, Elsevier, vol. 9(1), pages 27-33, January.
    • Handle: RePEc:eee:stapro:v:9:y:1990:i:1:p:27-33
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    Cited by:

    1. Dutta, Santanu & Goswami, Alok, 2013. "Pointwise and uniform convergence of kernel density estimators using random bandwidths," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2711-2720.

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