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Marginal integration M-estimators for additive models

Author

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  • Graciela Boente

    (Universidad de Buenos Aires and IMAS, CONICET, Ciudad Universitaria)

  • Alejandra Martínez

    (Universidad de Buenos Aires and IMAS, CONICET, Ciudad Universitaria)

Abstract

Additive regression models have a long history in multivariate non-parametric regression. They provide a model in which the regression function is decomposed as a sum of functions, each of them depending only on a single explanatory variable. The advantage of additive models over general non-parametric regression models is that they allow to obtain estimators converging at the optimal univariate rate avoiding the so-called curse of dimensionality. Beyond backfitting, marginal integration is a common procedure to estimate each component in additive models. In this paper, we propose a robust estimator of the additive components which combines local polynomials on the component to be estimated with the marginal integration procedure. The proposed estimators are consistent and asymptotically normally distributed. A simulation study allows to show the advantage of the proposal over the classical one when outliers are present in the responses, leading to estimators with good robustness and efficiency properties.

Suggested Citation

  • Graciela Boente & Alejandra Martínez, 2017. "Marginal integration M-estimators for additive models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 231-260, June.
    • Handle: RePEc:spr:testjl:v:26:y:2017:i:2:d:10.1007_s11749-016-0508-0
    DOI: 10.1007/s11749-016-0508-0
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    References listed on IDEAS

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