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Bias reduction in kernel density estimation via Lipschitz condition

Mynbaev, Kairat and Martins-Filho, Carlos (2009): Bias reduction in kernel density estimation via Lipschitz condition. Published in: Journal of Nonparametric Statistics , Vol. 22, No. 2 (February 2010): pp. 219-235.

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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 characterization 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.

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