Resistant dispersion estimation for nonparametric regression
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Ioannis Kalogridis [1] ; Stefan Van Aelst [2]
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[1] University of Glasgow
University of Glasgow
Reino Unido
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[2] KU Leuven
KU Leuven
Arrondissement Leuven, Bélgica
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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. 34, Nº. 3, 2025, págs. 660-690
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
Estimation of the dispersion of the errors is a central problem in regression analysis. An estimate of this dispersion is needed for most statistical inference procedures such as the construction of confidence intervals. In the context of robustness, it also plays a crucial role in the identification of outliers. Several nonparametric methods to estimate the dispersion function in heteroscedastic regression models have been proposed through the years. However, the vast majority of them rely on Gaussian likelihood and least-squares procedures, leading to estimators that are sensitive to atypical observations such as gross errors in the response space. To remedy this deficiency, a novel class of resistant nonparametric dispersion estimators is introduced and studied. This class of estimators builds upon the likelihood principle and spline smoothing. Estimators in this class can combine resistance towards atypical observations with high efficiency at the Gaussian model. It is shown that the new class of estimators is computationally efficient and enjoys optimal asymptotic properties. Its highly competitive performance is illustrated through a simulation study and a real-data example containing atypical observations.
