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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. © 2019, The Institute of Statistical Mathematics, Tokyo.

Registro:

Documento: Artículo
Título:Robust estimation in single-index models when the errors have a unimodal density with unknown nuisance parameter
Autor:Agostinelli, C.; Bianco, A.M.; Boente, G.
Filiación:Dipartimento di Matematica, Università di Trento, Via Sommarive, 14, Trento, 38123, Italy
Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and CONICET, Ciudad Universitaria, Pabellón 2, Buenos Aires, 1428, Argentina
Departamento de Matemáticas, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IMAS, CONICET, Ciudad Universitaria, Pabellón 1, Buenos Aires, 1428, Argentina
Palabras clave:Fisher consistency; Kernel weights; Local polynomials; Robustness; Single-index models; Errors; Robustness (control systems); Asymptotic distributions; Fisher consistency; K fold cross validations; Kernel weight; Local polynomials; Robustness properties; Single index models; Smoothing parameter; Parameter estimation
Año:2019
DOI: http://dx.doi.org/10.1007/s10463-019-00712-8
Título revista:Annals of the Institute of Statistical Mathematics
Título revista abreviado:Annal. Inst. Stat. Math.
ISSN:00203157
CODEN:AISXA
Registro:http://digital.bl.fcen.uba.ar/collection/paper/document/paper_00203157_v_n_p_Agostinelli

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Citas:

---------- APA ----------
Agostinelli, C., Bianco, A.M. & Boente, G. (2019) . Robust estimation in single-index models when the errors have a unimodal density with unknown nuisance parameter. Annals of the Institute of Statistical Mathematics.
http://dx.doi.org/10.1007/s10463-019-00712-8
---------- CHICAGO ----------
Agostinelli, C., Bianco, A.M., Boente, G. "Robust estimation in single-index models when the errors have a unimodal density with unknown nuisance parameter" . Annals of the Institute of Statistical Mathematics (2019).
http://dx.doi.org/10.1007/s10463-019-00712-8
---------- MLA ----------
Agostinelli, C., Bianco, A.M., Boente, G. "Robust estimation in single-index models when the errors have a unimodal density with unknown nuisance parameter" . Annals of the Institute of Statistical Mathematics, 2019.
http://dx.doi.org/10.1007/s10463-019-00712-8
---------- VANCOUVER ----------
Agostinelli, C., Bianco, A.M., Boente, G. Robust estimation in single-index models when the errors have a unimodal density with unknown nuisance parameter. Annal. Inst. Stat. Math. 2019.
http://dx.doi.org/10.1007/s10463-019-00712-8