Robust bandwidth selection in semiparametric partly linear regression models: Monte Carlo study and influential analysis

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In this paper, under a semiparametric partly linear regression model with fixed design, we introduce a family of robust procedures to select the bandwidth parameter. The robust plug-in proposal is based on nonparametric robust estimates of the νth derivatives and under mild conditions, it converges...

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Detalles Bibliográficos
Autor principal: Boente, G.
Otros Autores: Rodriguez, D.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: 2008
Acceso en línea:Registro en Scopus
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Biblioteca Central Dr. Luis F. Leloir (FCEN) de Universidad de Buenos Aires
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030 |a CSDAD 
100 1 |a Boente, G. 
245 1 0 |a Robust bandwidth selection in semiparametric partly linear regression models: Monte Carlo study and influential analysis 
260 |c 2008 
270 1 0 |m Boente, G.; Departamento de Matemáticas, Instituto de Cálculo, FCEyNArgentina; email: gboente@dm.uba.ar 
506 |2 openaire  |e Política editorial 
504 |a Aneiros-Pérez, G., Quintela del Río, G., Plug-in bandwidth choice in partial linear regression models with autoregressive errors (2002) J. Statist. Plann. Inference, 57, pp. 23-48 
504 |a Bianco, A., Boente, G., Robust estimators in semiparametric partly linear regression models (2004) J. Statist. Plann. Inference, 122, pp. 229-252 
504 |a Bianco, A., Boente, G., Robust estimators under a semiparametric partly linear autoregression model: asymptotic behavior and bandwidth selection (2007) J. Time Ser. Anal., 28, pp. 274-306 
504 |a Boente, G., Rodriguez, D., Robust estimators of high order derivatives of regression functions (2006) Statist. Probab. Lett., 76, pp. 1335-1344 
504 |a Boente, G., Fraiman, R., Meloche, J., Robust plug-in bandwidth estimators in nonparametric regression (1997) J. Statist. Plann. Inference, 57, pp. 109-142 
504 |a Cantoni, E., Ronchetti, E., Resistant selection of the smoothing parameter for smoothing splines (2001) Statist. Comput., 11, pp. 141-146 
504 |a Gasser, Th., Kneip, A., Köhler, W., A flexible and fast method for automatic smoothing (1991) J. Amer. Statist. Assoc., 86, pp. 643-652 
504 |a Härdle, W., Gasser, T., On robust kernel estimation of derivatives of regression functions (1985) Scand. J. Statist., 12, pp. 233-240 
504 |a Jiang, J., Mack, Y., Robust local polynomial regression for dependent data (2001) Statist. Sinica, 11, pp. 705-722 
504 |a Leung, D., Cross-validation in nonparametric regression with outliers (2005) Ann. Statist., 33, pp. 2291-2310 
504 |a Leung, D., Marriott, F., Wu, E., Bandwidth selection in robust smoothing (1993) J. Nonparametric Statist., 4, pp. 333-339 
504 |a Linton, O., Second order approximation in the partially linear regression model (1995) Econometrica, 63, pp. 1079-1112 
504 |a Manchester, L., Empirical influence for robust smoothing (1996) Austral. J. Statist., 38, pp. 275-296 
504 |a Maronna, R., Martin, R.D., Yohai, V., (2006) Robust Statistics: Theory and Practice, , Wiley, New York 
504 |a Rice, J., Convergence rates for partially splined models (1986) Statist. Probab. Lett., 4, pp. 203-208 
504 |a Robinson, P., Root-n-consistent semiparametric regression (1988) Econometrica, 56, pp. 931-954 
504 |a Ronchetti, E., Staudte, R., A robust version of Mallow's Cp (1994) J. Amer. Statist. Assoc., 89, pp. 550-559 
504 |a Rousseeuw, P.J., Least median of squares regression (1984) J. Amer. Statist. Assoc., 79, pp. 871-881 
504 |a Ruppert, D., Sheater, S., Wand, M., An effective bandwidth selector for local least squares regression (1995) J. Amer. Statist. Assoc., 90, pp. 1257-1270 
504 |a Speckman, P., Kernel smoothing in partial linear models (1988) J. Roy. Statist. Soc. Ser. B, 50, pp. 413-436 
504 |a Tukey, J., (1977) Exploratory Data Analysis, , Addison-Wesley, Reading, MA 
504 |a Wang, F., Scott, D., The L1 method for robust nonparametric regression (1994) J. Amer. Statist. Assoc., 89, pp. 65-76 
504 |a Welsh, A., Robust estimation of smooth regression and spread functions and their derivatives (1996) Statist. Sinica, 6, pp. 347-366 
520 3 |a In this paper, under a semiparametric partly linear regression model with fixed design, we introduce a family of robust procedures to select the bandwidth parameter. The robust plug-in proposal is based on nonparametric robust estimates of the νth derivatives and under mild conditions, it converges to the optimal bandwidth. A robust cross-validation bandwidth is also considered and the performance of the different proposals is compared through a Monte Carlo study. We define an empirical influence measure for data-driven bandwidth selectors and, through it, we study the sensitivity of the data-driven bandwidth selectors. It appears that the robust selector compares favorably to its classical competitor, despite the need to select a pilot bandwidth when considering plug-in bandwidths. Moreover, the plug-in procedure seems to be less sensitive than the cross-validation in particular, when introducing several outliers. When combined with the three-step procedure proposed by Bianco and Boente [2004. Robust estimators in semiparametric partly linear regression models. J. Statist. Plann. Inference 122, 229-252] the robust selectors lead to robust data-driven estimates of both the regression function and the regression parameter. © 2007 Elsevier B.V. All rights reserved.  |l eng 
536 |a Detalles de la financiación: Universidad de Buenos Aires, PID 5505 
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, PAV 120, PICT 21407 
536 |a Detalles de la financiación: The authors would like to thank the referee for its valuable comments and suggestions that lead to improve the presentation of the paper. This research was partially supported by Grants X-094 from the Universidad de Buenos Aires, PID 5505 from CONICET and PAV 120 and PICT 21407 from ANPCYT, Argentina. 
593 |a Departamento de Matemáticas, Instituto de Cálculo, FCEyN, Argentina 
690 1 0 |a ASYMPTOTIC PROPERTIES 
690 1 0 |a BANDWIDTH SELECTORS 
690 1 0 |a KERNEL WEIGHTS 
690 1 0 |a PARTLY LINEAR MODELS 
690 1 0 |a ROBUST ESTIMATION 
690 1 0 |a SMOOTHING TECHNIQUES 
690 1 0 |a ASYMPTOTIC ANALYSIS 
690 1 0 |a BANDWIDTH 
690 1 0 |a LINEAR REGRESSION 
690 1 0 |a MONTE CARLO METHODS 
690 1 0 |a PARAMETER ESTIMATION 
690 1 0 |a INFLUENTIAL ANALYSIS 
690 1 0 |a NONPARAMETRIC ROBUST ESTIMATES 
690 1 0 |a OPTIMAL BANDWIDTH 
690 1 0 |a ROBUST CONTROL 
700 1 |a Rodriguez, D. 
773 0 |d 2008  |g v. 52  |h pp. 2808-2828  |k n. 5  |p Comput. Stat. Data Anal.  |x 01679473  |w (AR-BaUEN)CENRE-4276  |t Computational Statistics and Data Analysis 
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856 4 0 |u https://doi.org/10.1016/j.csda.2007.10.017  |y DOI 
856 4 0 |u https://hdl.handle.net/20.500.12110/paper_01679473_v52_n5_p2808_Boente  |y Handle 
856 4 0 |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01679473_v52_n5_p2808_Boente  |y Registro en la Biblioteca Digital 
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962 |a info:eu-repo/semantics/article  |a info:ar-repo/semantics/artículo  |b info:eu-repo/semantics/publishedVersion 
999 |c 83425 

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