Robust estimates in generalized partially linear single-index models

A natural generalization of the well known generalized linear models is to allow only for some of the predictors to be modeled linearly while others are modeled nonparametrically. However, this model can face the so called "curse of dimensionality" problem that can be solved by imposing a...

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Detalles Bibliográficos
Autores principales: Boente, Graciela Lina, Rodríguez, Daniela Andrea
Publicado: 2012
Materias:
Asymptotic properties
Generalized partly linear single-index models
Rate of convergence
Robust estimation
Smoothing techniques
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_11330686_v21_n2_p386_Boente
http://hdl.handle.net/20.500.12110/paper_11330686_v21_n2_p386_Boente
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_11330686_v21_n2_p386_Boente
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spelling paper:paper_11330686_v21_n2_p386_Boente2023-06-08T16:09:09Z Robust estimates in generalized partially linear single-index models Boente, Graciela Lina Rodríguez, Daniela Andrea Asymptotic properties Generalized partly linear single-index models Rate of convergence Robust estimation Smoothing techniques A natural generalization of the well known generalized linear models is to allow only for some of the predictors to be modeled linearly while others are modeled nonparametrically. However, this model can face the so called "curse of dimensionality" problem that can be solved by imposing a nonparametric dependence on some unknown projection of the carriers. More precisely, we assume that the observations (y i,x i,t i),1≤i≤n, are such that t i∈ℝ q, x i∈ℝ p and y i{pipe}(x i,t i)~F({dot operator},μ i) with μ=(η(α Tt i+X i Tβ), for some known distribution function F and link function H. The function η:ℝ→ℝ and the parameters α and β are unknown and to be estimated. This model is known as the generalized partly linear single-index model. In this paper, we introduce a family of robust estimates for the parametric and nonparametric components under a generalized partially linear single-index model. It is shown that the estimates of α and β are root-n consistent and asymptotically normally distributed. Through a Monte Carlo study, we compare the performance of the proposed estimators with that of the classical ones. © 2011 Sociedad de Estadística e Investigación Operativa. Fil:Boente, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Rodriguez, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_11330686_v21_n2_p386_Boente http://hdl.handle.net/20.500.12110/paper_11330686_v21_n2_p386_Boente
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Asymptotic properties
Generalized partly linear single-index models
Rate of convergence
Robust estimation
Smoothing techniques
spellingShingle Asymptotic properties
Generalized partly linear single-index models
Rate of convergence
Robust estimation
Smoothing techniques
Boente, Graciela Lina
Rodríguez, Daniela Andrea
Robust estimates in generalized partially linear single-index models
topic_facet Asymptotic properties
Generalized partly linear single-index models
Rate of convergence
Robust estimation
Smoothing techniques
description A natural generalization of the well known generalized linear models is to allow only for some of the predictors to be modeled linearly while others are modeled nonparametrically. However, this model can face the so called "curse of dimensionality" problem that can be solved by imposing a nonparametric dependence on some unknown projection of the carriers. More precisely, we assume that the observations (y i,x i,t i),1≤i≤n, are such that t i∈ℝ q, x i∈ℝ p and y i{pipe}(x i,t i)~F({dot operator},μ i) with μ=(η(α Tt i+X i Tβ), for some known distribution function F and link function H. The function η:ℝ→ℝ and the parameters α and β are unknown and to be estimated. This model is known as the generalized partly linear single-index model. In this paper, we introduce a family of robust estimates for the parametric and nonparametric components under a generalized partially linear single-index model. It is shown that the estimates of α and β are root-n consistent and asymptotically normally distributed. Through a Monte Carlo study, we compare the performance of the proposed estimators with that of the classical ones. © 2011 Sociedad de Estadística e Investigación Operativa.
author Boente, Graciela Lina
Rodríguez, Daniela Andrea
author_facet Boente, Graciela Lina
Rodríguez, Daniela Andrea
author_sort Boente, Graciela Lina
title Robust estimates in generalized partially linear single-index models
title_short Robust estimates in generalized partially linear single-index models
title_full Robust estimates in generalized partially linear single-index models
title_fullStr Robust estimates in generalized partially linear single-index models
title_full_unstemmed Robust estimates in generalized partially linear single-index models
title_sort robust estimates in generalized partially linear single-index models
publishDate 2012
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_11330686_v21_n2_p386_Boente
http://hdl.handle.net/20.500.12110/paper_11330686_v21_n2_p386_Boente
work_keys_str_mv AT boentegracielalina robustestimatesingeneralizedpartiallylinearsingleindexmodels
AT rodriguezdanielaandrea robustestimatesingeneralizedpartiallylinearsingleindexmodels
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