JSM 2004 - Toronto

Abstract #301938

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Activity Number: 268
Type: Topic Contributed
Date/Time: Tuesday, August 10, 2004 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #301938
Title: Data Sharpening under Unimodal Constraint in Kernel Density Estimation
Author(s): Kee-Hoon Kang*+ and Peter Hall
Companies: Hankuk University of Foreign Studies and Australian National University
Address: Mohyun, Yongin, 449-791, Korea
Keywords: unimodal density ; data sharpening ; density estimation
Abstract:

We discuss a robust data-sharpening method for rendering a standard kernel estimator, with a given bandwidth, unimodal. It has theoretical and numerical properties of the type that one would like such a technique to enjoy. In particular, we show theoretically that, with probability converging to~1 as sample size diverges, our technique alters the kernel estimator only in places where the latter has spurious bumps, and is identical to the kernel estimator in places where that estimator is monotone in the correct direction. Moreover, it automatically splices together, in a smooth and seamless way, those parts of the estimator that it leaves unchanged and those that it adjusts. Provided the true density is unimodal our estimator generally reduces mean integrated squared error of the standard kernel estimator.

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