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# Automatic Smoothing Spline Projection Pursuit

Charles B. Roosen and Trevor J. Hastie
Journal of Computational and Graphical Statistics
Vol. 3, No. 3 (Sep., 1994), pp. 235-248
DOI: 10.2307/1390909
Stable URL: http://www.jstor.org/stable/1390909
Page Count: 14
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## Abstract

A highly flexible nonparametric regression model for predicting a response y given covariates {xk}k=1d is the projection pursuit regression (PPR) model ŷ = h(x) = $\beta _{0}+\sum_{j}\beta _{j}f_{j}(\boldsymbol{\alpha}_{j}^{T}\mathbf{\mathit{x}})$, where the fj are general smooth functions with mean 0 and norm 1, and ∑k=1dα kj2=1. The standard PPR algorithm of Friedman and Stuetzle (1981) estimates the smooth functions fj using the supersmoother nonparametric scatterplot smoother. Friedman's algorithm constructs a model with Mmax linear combinations, then prunes back to a simpler model of size M≤ Mmax, where M and Mmax are specified by the user. This article discusses an alternative algorithm in which the smooth functions are estimated using smoothing splines. The direction coefficients α j, the amount of smoothing in each direction, and the number of terms M and Mmax are determined to optimize a single generalized cross-validation measure.

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