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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Autor principal: Boente, G.
Otros Autores: Rodriguez, D.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: 2012
Acceso en línea:Registro en Scopus
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100 1 |a Boente, G. 
245 1 0 |a Robust estimates in generalized partially linear single-index models 
260 |c 2012 
270 1 0 |m Rodriguez, D.; Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and CONICET, Ciudad Universitaria, Pabellón 2, Buenos Aires 1428, Argentina; email: drodrig@dm.uba.ar 
506 |2 openaire  |e Política editorial 
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504 |a Boente, G., Rodriguez, D., Robust inference in generalized partially linear models (2010) Comput Stat Data Anal, 54, pp. 2942-2966 
504 |a Boente, G., He, X., Zhou, J., Robust estimates in generalized partially linear models (2006) Ann Stat, 34, pp. 2856-2878 
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504 |a Carroll, R., Fan, J., Gijbels, I., Wand, M., Generalized partially linear single-index models (1997) J Am Stat Assoc, 92, pp. 477-489 
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504 |a Rodriguez, D., (2008) Doctoral thesis, Universidad de Buenos Aires, , http://cms.dm.uba.ar/academico/carreras/doctorado/tesisdanielarodriguez.pdf, Available at 
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520 3 |a 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.  |l eng 
536 |a Detalles de la financiación: Universidad de Buenos Aires, PID 112-200801-00216 
536 |a Detalles de la financiación: Agencia Nacional de Promoción Científica y Tecnológica 
536 |a Detalles de la financiación: Consejo Nacional de Investigaciones Científicas y Técnicas, PICT m 821 
536 |a Detalles de la financiación: Acknowledgements This research was partially supported by Grants X018 from Universidad of Buenos Aires, PID 112-200801-00216 from CONICET and PICT m 821 from ANPCYT, Argentina. The authors thank Matt Wand for providing the code to compute the estimators defined in Carroll et al. (1997). We also wish to thank two anonymous referees and the Associate Editor for valuable comments which led to an improved version of the original paper. 
593 |a Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and CONICET, Ciudad Universitaria, Pabellón 2, Buenos Aires 1428, Argentina 
690 1 0 |a ASYMPTOTIC PROPERTIES 
690 1 0 |a GENERALIZED PARTLY LINEAR SINGLE-INDEX MODELS 
690 1 0 |a RATE OF CONVERGENCE 
690 1 0 |a ROBUST ESTIMATION 
690 1 0 |a SMOOTHING TECHNIQUES 
700 1 |a Rodriguez, D. 
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