JSM 2004 - Toronto

Abstract #301453

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Activity Number: 378
Type: Contributed
Date/Time: Wednesday, August 11, 2004 : 2:00 PM to 3:50 PM
Sponsor: General Methodology
Abstract - #301453
Title: On Nonparametric Density Estimation Near the Boundary
Author(s): R. J. Karunamuni*+
Companies: University of Alberta
Address: Dept. of Math. & Stat. Sciences, Edmonton, AB, T6G 2G1, Canada
Keywords: density estimation ; mean squared error ; kernel estimation ; reflection ; transformation
Abstract:

The kernel method of estimation of curves is now popular and widely used in statistical applications. Kernel estimators suffer from boundary effects however, when the support of the function to be estimated has finite endpoints. Boundary effects seriously affect the overall performance of the estimator. A number of solutions (adjustments and modifications) have been proposed with some success. We develop a new general method of boundary correction for kernel density estimation. Our technique is a kind of generalized reflection involving transformed data. The proposed method generates a class of boundary corrected estimators. They all possess desirable properties such as local adaptivity and the non-negativity. The theory behind the new methodology along with the bias and variance of the proposed estimators are presented. Results of a data analysis are also given.

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