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

Author

Listed:
  • Claudio Agostinelli

    (Università di Trento)

  • Ana M. Bianco

    (Universidad de Buenos Aires and CONICET)

  • Graciela Boente

    (Universidad de Buenos Aires and IMAS, CONICET)

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.

Suggested Citation

  • Claudio Agostinelli & Ana M. Bianco & Graciela Boente, 2020. "Robust estimation in single-index models when the errors have a unimodal density with unknown nuisance parameter," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 855-893, June.
    • Handle: RePEc:spr:aistmt:v:72:y:2020:i:3:d:10.1007_s10463-019-00712-8
    DOI: 10.1007/s10463-019-00712-8
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    References listed on IDEAS

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