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Marron, J.S. and Ruppert, D. (1992) Transformations to Reduce Boundary Bias in Kernel Density Estimation. Journal of the Royal Statistical Society: Series B, 4, 653-671.

has been cited by the following article:

• TITLE: Some Improvement on Convergence Rates of Kernel Density Estimator

  AUTHORS: Xiaoran Xie, Jingjing Wu

  KEYWORDS: Kernel Density Estimation, Geometric Extrapolation, Bias Reduction, Mean Squared Error, Convergence Rate

  JOURNAL NAME: Applied Mathematics, Vol.5 No.11, June 20, 2014

  ABSTRACT: In this paper two kernel density estimators are introduced and investigated. In order to reduce bias, we intuitively subtract an estimated bias term from ordinary kernel density estimator. The second proposed density estimator is a geometric extrapolation of the first bias reduced estimator. Theoretical properties such as bias, variance and mean squared error are investigated for both estimators. To observe their finite sample performance, a Monte Carlo simulation study based on small to moderately large samples is presented.