Marginal integration M-estimators for additive models
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Graciela Boente [1] ; Alejandra Martínez [1]
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[1] Universidad de Buenos Aires
Universidad de Buenos Aires
Argentina
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- Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 26, Nº. 2, 2017, págs. 231-260
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
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.
