SFB 303 Discussion Paper No. A - 107
Author: Härdle, Wolfgang, and Thomas M. Stoker
Title: Investigating Smooth Multiple Regression by the Method of Average Derivatives
Abstract: A common approach to representing nonlinear dependencies in regression analysis is to model the mean
response variable as a nonlinear function of a weighted sum of the predictor variables. Knowledge of the
coefficients, or weights of this sum, will often suffice for practical questions of interest, such as the relative
strengths of the influences of the predictor variable coordinates. In this paper we show how to determine these
coefficients (up to scale) without specifying the nonlinear function, using the method of average derivatives.
Moreover, we propose a procedure for characterizing general multiple regression relationships based on a
weighted sum of the predictor variable coordinates. The procedure provides a computationally simple alternative
to projection pursuit regression (PPR) of Friedman and Stuetzle (1981), and other techniques, such as the
iterative ACE algorithm of Breiman and Friedman (1985).
Creation-Date: February 1987
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