Abstract #301720

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JSM 2003 Abstract #301720
Activity Number: 245
Type: Contributed
Date/Time: Tuesday, August 5, 2003 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #301720
Title: Kernel Regression Trees: Recursive Partitioning of Bandwidths for Local-Linear Smoothing
Author(s): William R. Schucany*+ and An Jia
Companies: Southern Methodist University and Southern Methodist University
Address: Dept. of Statistical Science, Dallas, TX, 75275-0332,
Keywords: local polynomial fits ; AIC ; variable bandwidths
Abstract:

For nonparametric regression problems with complicated structure, a single global smoothing parameter is unsatisfactory. Specifically, kernel estimators of conditional response means can be improved by adapting to local curvature. Locally weighted least squares polynomial fits have been shown by others to be successful. However, estimates of variable bandwidths can be a challenging undertaking. We have previously made some satisfactory progress with piecewise constant bandwidths for local linear fitting and a modified Akaike Information Criterion. Our new proposal extends this approach with a recursive partitioning to simultaneously determine both the interval in the explanatory variable and the bandwidth to be used throughout that interval. The result is a regression tree with separate data-based estimates of the kernel smoothing parameters, which are applied over adaptively selected regions in the predictor variable. The new methodology compares well with the variable bandwidth estimators.

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