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
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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
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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
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DOI: |
http://dx.doi.org/10.1007/s10463-019-00712-8 |
Título revista: | Annals of the Institute of Statistical Mathematics
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Título revista abreviado: | Annal. Inst. Stat. Math.
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ISSN: | 00203157
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CODEN: | AISXA
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Registro: | https://bibliotecadigital.exactas.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