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On a certain class of nonparametric density estimators with reduced bias

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  • Naito, Kanta

Abstract

A class of kernel-based nonparametric density estimators with reduced bias is considered which is constructed from a multiplicative adjustment scheme. Estimators in the class are connected by a real parameter [alpha] and an interesting fact is that the leading term of the bias is linear in [alpha] and that of the variance is free for [alpha]. This shows that the asymptotic mean integrated squared error is quadratic in [alpha]. Consequently, we can find the best estimator in the class. Suggestions for practical choices of [alpha] are given.

Suggested Citation

  • Naito, Kanta, 2001. "On a certain class of nonparametric density estimators with reduced bias," Statistics & Probability Letters, Elsevier, vol. 51(1), pages 71-78, January.
    • Handle: RePEc:eee:stapro:v:51:y:2001:i:1:p:71-78
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    Cited by:

    1. Okumura, Hidenori & Naito, Kanta, 2006. "Non-parametric kernel regression for multinomial data," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 2009-2022, October.
    2. Naito, Kanta & Yoshizaki, Masahiro, 2009. "Bandwidth selection for a data sharpening estimator in nonparametric regression," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1465-1486, August.

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