Robust estimation in single-index models when the errors have a unimodal density with unknown nuisance parameter

Claudio Agostinelli (), Ana M. Bianco () and Graciela Boente ()
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Claudio Agostinelli: Università di Trento
Ana M. Bianco: Universidad de Buenos Aires and CONICET
Graciela Boente: Universidad de Buenos Aires and IMAS, CONICET

Annals of the Institute of Statistical Mathematics, 2020, vol. 72, issue 3, No 9, 855-893

Abstract: Abstract This paper develops a robust profile estimation method for the parametric and nonparametric components of a single-index model when the errors have a strongly unimodal density with unknown nuisance parameter. We derive consistency results for the link function estimators as well as consistency and asymptotic distribution results for the single-index parameter estimators. Under a log-Gamma model, the sensitivity to anomalous observations is studied using the empirical influence curve. We also discuss a robust K-fold cross-validation procedure to select the smoothing parameters. A numerical study carried on with errors following a log-Gamma model and for contaminated schemes shows the good robustness properties of the proposed estimators and the advantages of considering a robust approach instead of the classical one. A real data set illustrates the use of our proposal.

Keywords: Kernel weights; Fisher consistency; Local polynomials; Single-index models; Robustness (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10463-019-00712-8

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