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Robust estimation in single-index models when the errors have a unimodal density with unknown nuisance parameter. (English) Zbl 07205441
Summary: 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.

##### MSC:
 62G35 Nonparametric robustness 62G07 Density estimation 62P10 Applications of statistics to biology and medical sciences; meta analysis 62P20 Applications of statistics to economics
robustbase
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