Abstract #300397

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JSM 2003 Abstract #300397
Activity Number: 331
Type: Contributed
Date/Time: Wednesday, August 6, 2003 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract - #300397
Title: The Use of Least-Squares Approximating Polynomials in Nonparametric Regression and Density Estimation
Author(s): Serge B. Provost*+
Companies: University of Western Ontario
Address: Dept. of Stat. & Actuarial Sciences, London, ON, N6A 5B7, Canada
Keywords: density estimation ; density approximation ; regression ; subsamples ; polynomial approximation ; nonparametric statistics
Abstract:

First, it is shown that certain density estimates (histogram and kernel types) that are based on substantially overlapping subsamples of a data set, are indeed adaptive. These estimates are then approximated by means of least-squares approximating polynomials--defined to be those minimizing the integrated squared error. The proposed density estimation methodologies are applied to a mixture of two Beta distributions as well as to the "Buffalo Snowfall" and the "Lengths of Treatment Spells" datasets. A regression method that also relies on least-squares approximating polynomials is introduced as well. This technique is illustrated with the "Motorcycle Helmet Impact" data.

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