On nonparametric local inference for density estimation

Authors:
Ngai-Hang Chan;Thomas C. M. Lee;Liang Peng
Affiliations:
Department of Statistics, The Chinese University of Hong Kong, Hong Kong;Department of Statistics, The Chinese University of Hong Kong, Hong Kong and Department of Statistics, Colorado State University, United States;School of Mathematics, Georgia Institute of Technology, United States
Venue:
Computational Statistics & Data Analysis
Year:
2010

Citing 3
Cited 1

An improved data-based algorithm for choosing the window width when estimating the density at a point

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Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems

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A data-based algorithm for choosing the window width when estimating the density at a point

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New approaches to nonparametric density estimation and selection of smoothing parameters

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Abstract

Bandwidth selection has been an important topic in nonparametric density estimation. In this paper an effective method for local bandwidth selection is proposed. For local bandwidth selection, due to data sparsity and other reasons, extremely small bandwidths are sometimes selected, which lead to severe undersmoothing. To circumvent this difficulty, the main idea behind the proposed method is to choose the largest bandwidth that still achieves the optimal rate. When coupled with practical bias reduction techniques, the bandwidth selected from this method can be applied simultaneously to conduct both local point and interval estimation. Simulation studies demonstrate the effectiveness of the proposed approach, which compares favorably with other existing approaches.