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Bias reduction in kernel density estimation via Lipschitz condition

Kairat Mynbaev () and Carlos Martins-Filho

Journal of Nonparametric Statistics, 2010, vol. 22, issue 2, 219-235

Abstract: In this paper we propose a new nonparametric kernel-based estimator for a density function f which achieves bias reduction relative to the classical Rosenblatt–Parzen estimator. Contrary to some existing estimators that provide for bias reduction, our estimator has a full asymptotic characterisation including uniform consistency and asymptotic normality. In addition, we show that bias reduction can be achieved without the disadvantage of potential negativity of the estimated density – a deficiency that results from using higher order kernels. Our results are based on imposing global Lipschitz conditions on f and defining a novel corresponding kernel. A Monte Carlo study is provided to illustrate the estimator's finite sample performance.

Date: 2010
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DOI: 10.1080/10485250903266058

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