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Abstract:

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.

Registro:

Documento: Artículo
Título:Robust estimates in generalized partially linear single-index models
Autor:Boente, G.; Rodriguez, D.
Filiación:Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and CONICET, Ciudad Universitaria, Pabellón 2, Buenos Aires 1428, Argentina
Palabras clave:Asymptotic properties; Generalized partly linear single-index models; Rate of convergence; Robust estimation; Smoothing techniques
Año:2012
Volumen:21
Número:2
Página de inicio:386
Página de fin:411
DOI: http://dx.doi.org/10.1007/s11749-011-0249-z
Título revista:Test
Título revista abreviado:Test
ISSN:11330686
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_11330686_v21_n2_p386_Boente

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Citas:

---------- APA ----------
Boente, G. & Rodriguez, D. (2012) . Robust estimates in generalized partially linear single-index models. Test, 21(2), 386-411.
http://dx.doi.org/10.1007/s11749-011-0249-z
---------- CHICAGO ----------
Boente, G., Rodriguez, D. "Robust estimates in generalized partially linear single-index models" . Test 21, no. 2 (2012) : 386-411.
http://dx.doi.org/10.1007/s11749-011-0249-z
---------- MLA ----------
Boente, G., Rodriguez, D. "Robust estimates in generalized partially linear single-index models" . Test, vol. 21, no. 2, 2012, pp. 386-411.
http://dx.doi.org/10.1007/s11749-011-0249-z
---------- VANCOUVER ----------
Boente, G., Rodriguez, D. Robust estimates in generalized partially linear single-index models. Test. 2012;21(2):386-411.
http://dx.doi.org/10.1007/s11749-011-0249-z