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February 1998 Projection estimation in multiple regression with application to functional ANOVA models
Jianhua Z. Huang
Ann. Statist. 26(1): 242-272 (February 1998). DOI: 10.1214/aos/1030563984

Abstract

A general theory on rates of convergence of the least-squares projection estimate in multiple regression is developed. The theory is applied to the functional ANOVA model, where the multivariate regression function is modeled as a specified sum of a constant term, main effects (functions of one variable) and selected interaction terms (functions of two or more variables). The least-squares projection is onto an approximating space constructed from arbitrary linear spaces of functions and their tensor products respecting the assumed ANOVA structure of the regression function. The linear spaces that serve as building blocks can be any of the ones commonly used in practice: polynomials, trigonometric polynomials, splines, wavelets and finite elements. The rate of convergence result that is obtained reinforces the intuition that low-order ANOVA modeling can achieve dimension reduction and thus overcome the curse of dimensionality. Moreover, the components of the projection estimate in an appropriately defined ANOVA decomposition provide consistent estimates of the corresponding components of the regression function. When the regression function does not satisfy the assumed ANOVA form, the projection estimate converges to its best approximation of that form.

Citation

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Jianhua Z. Huang. "Projection estimation in multiple regression with application to functional ANOVA models." Ann. Statist. 26 (1) 242 - 272, February 1998. https://doi.org/10.1214/aos/1030563984

Information

Published: February 1998
First available in Project Euclid: 28 August 2002

zbMATH: 0930.62042
MathSciNet: MR1611780
Digital Object Identifier: 10.1214/aos/1030563984

Subjects:
Primary: 62G07
Secondary: 62G20

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.26 • No. 1 • February 1998
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