Artículo

Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

In many applications of regression analysis, there are covariates that are measured with errors. A robust family of estimators of the parametric and nonparametric components of a structural partially linear errors-in-variables model is introduced. The proposed estimators are based on a three-step procedure where robust orthogonal regression estimators are combined with robust smoothing techniques. Under regularity conditions, it is proved that the resulting estimators are consistent. The robustness of the proposal is studied by means of the empirical influence function when the linear parameter is estimated using the orthogonal M-estimator. A simulation study allows to compare the behaviour of the robust estimators with their classical relatives and a real example data is analysed to illustrate the performance of the proposal. © 2016 Elsevier B.V.

Registro:

Documento: Artículo
Título:Robust estimation in partially linear errors-in-variables models
Autor:Bianco, A.M.; Spano, P.M.
Filiación:Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and CONICET, Ciudad Universitaria, Buenos Aires, Argentina
Departamento de Ciencias Exactas, Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria, Buenos Aires, Argentina
Palabras clave:Fisher-consistency; Kernel weights; M-location functionals; Nonparametric regression; Robust estimation; Errors; Orthogonal functions; Regression analysis; Fisher-consistency; Functionals; Kernel weight; Non-parametric regression; Robust estimation; Parameter estimation
Año:2017
Volumen:106
Página de inicio:46
Página de fin:64
DOI: http://dx.doi.org/10.1016/j.csda.2016.09.002
Título revista:Computational Statistics and Data Analysis
Título revista abreviado:Comput. Stat. Data Anal.
ISSN:01679473
CODEN:CSDAD
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01679473_v106_n_p46_Bianco

Referencias:

  • Afifi, A.A., Azen, S.P., Statistical Analysis: A Computer Oriented Approach (1979), Academic Press New York and London; Aït Sahalia, Y., The delta method for nonaparmetric kernel functionals (1995), (Ph.D. dissertation) University of Chicago; Bianco, A., Boente, G., Robust estimators in semiparametric partly linear regression models (2004) J. Statist. Plann. Inference, 122, pp. 229-252
  • Bianco, A., Boente, G., Robust estimators under semi-parametric partly linear autoregression: Asymptotic behaviour and bandwidth selection (2007) J. Time Series Anal., 28, pp. 274-306
  • Boente, G., Fraiman, R., Robust nonparametric regression estimation for dependent observations (1990) Ann. Statist., 17, pp. 1242-1256
  • Boente, G., Fraiman, R., Strong uniform convergence rates for some robust equivariant nonparametric regression estimates for mixing processes (1991) Internat. Statist. Rev., 59, pp. 355-372
  • Boente, G., Rodriguez, D., Robust inference in generalized partially linear models (2010) Comput. Statist. Data Anal., 54, pp. 2942-2966
  • Buonaccorsi, J.P., Measurement Error: Models, Methods and Applications (2010), Chapman and Hall /CRC USA; Carroll, R.J., Ruppert, D., Stefanski, L.A., Measurement Error in Nonlinear Models (1995), Chapman and Hall London; Croux, C., Fekri, M., Ruiz-Gazen, A., Fast and robust estimation of the multivariate errors in variables model (2010) TEST, 19, pp. 286-303
  • Cui, H., Kong, E., Empirical likelihood confidence region for parameters in semi-linear errors-in-variables models (2006) Scand. J. Stat., 33, pp. 153-168
  • Fekri, M., Ruiz-Gazen, A., Robust weighted orthogonal regression in the errors-in-variables model (2004) J. Multivariate Anal., 88, pp. 89-108
  • Fuller, W.A., Measurement Error Models (1987), Wiley New York; Hampel, F.R., The influence curve and its role in robust estimation (1974) J. Amer. Statist. Assoc., 69, pp. 383-394
  • Härdle, W., Robust regression function estimation (1984) J. Multivariate Anal., 14, pp. 169-180
  • Härdle, W., Liang, H., Gao, J., Partially Linear Models (2000), Physica–Verlag; He, X., Liang, H., Quantile regression estimates for a class of linear and partially linear errorsin-variables models (2000) Statist. Sinica, 10, pp. 129-140
  • He, X., Zhu, Z., Fung, W., Estimation in a semiparametric model for longitudinal data with unspecified dependence structure (2002) Biometrika, 89, pp. 579-590
  • Liang, H., Asymptotic normality of parametric part in partially linear model with measurement error in the non-parametric part (2000) J. Statist. Plann. Inference, 86, pp. 51-62
  • Liang, H., Härdle, W., Carroll, R.J., Estimation in a semiparametric partially linear errors–in–variables model (1999) Ann. Statist., 27, pp. 1519-1535
  • Liang, H., Li, R., Variable selection for partially linear models with measurement errors (2009) J. Amer. Statist. Assoc., 104, pp. 234-248
  • Liang, H., Wang, S., Carroll, R.J., Partially linear models with missing response variables and error-prone covariates (2007) Biometrika, 94, pp. 185-198
  • Ma, Y., Carroll, R.J., Locally efficient estimators for semiparametric models with measurement error (2006) J. Amer. Statist. Assoc., 101, pp. 1465-1474
  • Mallows, C., On some topics in robustness (1974), Memorandum, Bell Laboratories, Murray Hill, NJ; Manchester, L., Empirical influence for robust smoothing (1996) Austral. J. Statist., 38, pp. 275-296
  • Maronna, R., Yohai, V.J., Correcting MM-estimates for fat data sets (2010) J. Comput. Statist. Data Anal., 54, pp. 3168-3173
  • Pan, W., Zeng, D., Lin, X., Estimation in semiparametric transition measurement error models for longitudinal data (2008) Biometrics, 65, pp. 728-736
  • Severini, T., Staniswalis, J., Quasi-likelihood estimation in semiparametric models (1994) J. Amer. Statist. Assoc., 89, pp. 501-511
  • Tamine, J., Smoothed influence function: another view at robust nonparametric regression (2002), Discussion paper 62, Sonderforschungsbereich 373, Humboldt-Universitat zu Berlin; Tukey, J., Exploratory Data Analysis (1977), Addison-Wesley Reading, MA; Zamar, R., Robust estimation in the errors–in–variables model (1989) Biometrika, 76, pp. 149-160
  • Zhu, L.X., Cui, H.J., A semi-parametric regression model with errors in the variables (2003) Scand. J. Stat., 30, pp. 429-442

Citas:

---------- APA ----------
Bianco, A.M. & Spano, P.M. (2017) . Robust estimation in partially linear errors-in-variables models. Computational Statistics and Data Analysis, 106, 46-64.
http://dx.doi.org/10.1016/j.csda.2016.09.002
---------- CHICAGO ----------
Bianco, A.M., Spano, P.M. "Robust estimation in partially linear errors-in-variables models" . Computational Statistics and Data Analysis 106 (2017) : 46-64.
http://dx.doi.org/10.1016/j.csda.2016.09.002
---------- MLA ----------
Bianco, A.M., Spano, P.M. "Robust estimation in partially linear errors-in-variables models" . Computational Statistics and Data Analysis, vol. 106, 2017, pp. 46-64.
http://dx.doi.org/10.1016/j.csda.2016.09.002
---------- VANCOUVER ----------
Bianco, A.M., Spano, P.M. Robust estimation in partially linear errors-in-variables models. Comput. Stat. Data Anal. 2017;106:46-64.
http://dx.doi.org/10.1016/j.csda.2016.09.002