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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