Marginal integration M-estimators for additive models

TEST volume 26, pages231–260(2017)Cite this article

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.

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Acknowledgments

The authors wish to thank the Associate Editor and two anonymous referees for valuable comments which led to an improved version of the original paper. This research was partially supported by Grants pip 112-201101-00339 from the Consejo Nacional de Investigaciones Científicas y Técnicas, pict 2014-0351 from the Agencia Nacional de Promoción Científica y Tecnológica and 20120130100279BA from the Universidad de Buenos Aires at Buenos Aires, Argentina.

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Affiliations

  1. Departamento de Matemáticas, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IMAS, CONICET, Ciudad Universitaria, Pabellón 1, 1428, Buenos Aires, Argentina

    Graciela Boente & Alejandra Martínez

Authors
  1. Graciela Boente
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  2. Alejandra Martínez
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Corresponding author

Correspondence to Graciela Boente.

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Boente, G., Martínez, A. Marginal integration M-estimators for additive models. TEST 26, 231–260 (2017). https://doi.org/10.1007/s11749-016-0508-0

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Keywords

  • Additive models
  • Local M-estimation
  • Kernel weights
  • Marginal integration
  • Robustness

Mathematics Subject Classification

  • 62G35
  • 62G20
  • 62G05