The Annals of Statistics

On Projection Pursuit Regression

Peter Hall

Full-text: Open access

Abstract

We construct a tractable mathematical model for kernel-based projection pursuit regression approximation. The model permits computation of explicit formulae for bias and variance of estimators. It is shown that the bias of an orientation estimate dominates error about the mean--indeed, the latter is asymptotically negligible in comparison with bias. However, bias and error about the mean are of the same order in the case of projection pursuit curve estimates. Implications of our formulae for bias and variance are discussed.

Article information

Source
Ann. Statist. Volume 17, Number 2 (1989), 573-588.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176347126

Digital Object Identifier
doi:10.1214/aos/1176347126

Mathematical Reviews number (MathSciNet)
MR994251

Zentralblatt MATH identifier
0698.62041

JSTOR
links.jstor.org

Subjects
Primary: 62H99: None of the above, but in this section
Secondary: 62H05: Characterization and structure theory

Keywords
Bias kernel method nonparametric regression orientation projection pursuit

Citation

Hall, Peter. On Projection Pursuit Regression. Ann. Statist. 17 (1989), no. 2, 573--588. doi:10.1214/aos/1176347126. http://projecteuclid.org/euclid.aos/1176347126.


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