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Functional ANOVA Models for Generalized Regression

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  • Huang, Jianhua Z.
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    Abstract

    The Functional ANOVA model is considered in the context of generalized regression, which includes logistic regression, probit regression, and Poisson regression as special cases. The multivariate predictor function is modeled as a specified sum of a constant term, main effects, and selected interaction terms. Maximum likelihood estimate is used, where the maximization is taken over a suitably chosen approximating space. The approximating space is constructed from virtually arbitrary linear spaces of functions and their tensor products and is compatible with the assumed ANOVA structure on the predictor function. Under mild conditions, the maximum likelihood estimate is consistent and the components of the estimate in an appropriately defined ANOVA decomposition are consistent in estimating the corresponding components of the predictor function. When the predictor function does not satisfy the assumed ANOVA form, the estimate converges to its best approximation of that form relative to the expected log-likelihood. A rate of convergence result is obtained, which reinforces the intuition that low-order ANOVA modeling can achieve dimension reduction and thus overcome the curse of dimensionality.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 67 (1998)
    Issue (Month): 1 (October)
    Pages: 49-71

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    Handle: RePEc:eee:jmvana:v:67:y:1998:i:1:p:49-71

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    Related research

    Keywords: Exponential family interaction maximum likelihood estimate rate of convergence splines tensor product;

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    Cited by:
    1. Huang, Jianhua Z., 2003. "Asymptotics for polynomial spline regression under weak conditions," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 207-216, November.
    2. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.

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