Abstract #301622

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JSM 2003 Abstract #301622
Activity Number: 245
Type: Contributed
Date/Time: Tuesday, August 5, 2003 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #301622
Title: Smooth Location Dependent Bandwidth Selection in Local Polynomial Regression
Author(s): Ilya Gluhovsky*+
Companies: Sun Microsystems Laboratories
Address: 2600 Casey Ave., Mountain View, CA, 94043,
Keywords: local regression ; bandwidth selection ; smoothness penalty ; spline ; MISE
Abstract:

It has been widely shown that the quality of prediction using local polynomial regression models critically depends on the choice of the kernel bandwidth. Several methods have been proposed to adaptively select a location dependent bandwidth function. The methods are usually based on minimizing a mean integrated squared error estimate (MISE), although other criteria, such as intersection of confidence intervals are also used. We tackle the issue of producing smooth (e.g. twice differentiable) fits. The issue arizes from the fact that a rough bandwidth function may result in rough estimates. In the proposed method, we put together a criterion that is a combination of fit and smoothness penalties. The former penalizes departures from the original bandwidth selection criterion, such as the MISE, while the latter penalizes roughness of the target function (as opposed to roughness of the bandwidth function). The criterion is minimized over spline bandwidth functions.

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