Asymptotic behavior of robust estimators in partially linear models with missing responses: The effect of estimating the missing probability on the simplified marginal estimators
In this paper, we consider a semiparametric partially linear regression model where missing data occur in the response. We derive the asymptotic behavior of the robust estimators for the regression parameter and of the weighted simplified location estimator introduced in Bianco et al. (Comput. Stat....
Guardado en:
| Autor principal: | |
|---|---|
| Otros Autores: | , , |
| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
| Publicado: |
2011
|
| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
| Sumario: | In this paper, we consider a semiparametric partially linear regression model where missing data occur in the response. We derive the asymptotic behavior of the robust estimators for the regression parameter and of the weighted simplified location estimator introduced in Bianco et al. (Comput. Stat. Data Anal. 54:546-564, 2010a). For the latter, consistency results and the asymptotic distribution are derived when the missing probability is known and also when it is estimated. © 2010 Sociedad de Estadística e Investigación Operativa. |
|---|---|
| Bibliografía: | Bianco, A., Boente, G., Robust estimators in semiparametric partly linear regression models (2004) J Stat Plan Inference, 122, pp. 229-252 Bianco, A., Martínez, E., Robust testing in the logistic regression model (2009) Comput Stat Data Anal, 53, pp. 4095-4105 Bianco, A., Yohai, V., (1996) Robust Estimation in the Logistic Regression Model, 109, pp. 17-34. , Lecture notes in statistics, New York: Springer Bianco, A., Boente, G., González-Manteiga, W., Pérez-González, A., Estimation of the marginal location under a partially linear model with missing responses (2010) Comput Stat Data Anal, 54, pp. 546-564 Bianco, A., Boente, G., González-Manteiga, W., Pérez-González, A., (2010) Asymptotic Behavior of Robust Estimators In Partially Linear Models With Missing Responses: The Effect of Estimating the Missing Probability On the Simplified Marginal Estimators, , http://eio.usc.es/eipc1/BASE/BASEMASTER/FORMULARIOS-PHP-DPTO/REPORTS/10-01.pdf, Report 10-01. Reports in statistics and operations research. Universidad de Santiago de Compostela Boente, G., He, X., Zhou, J., Robust estimates in generalized partially linear models (2006) Ann Stat, 34, pp. 2856-2878 Boente, G., González-Manteiga, W., Pérez-González, A., Robust nonparametric estimation with missing data (2009) J Stat Plan Inference, 139, pp. 571-592 Croux, C., Haesbroeck, G., Implementing the Bianco and Yohai estimator for logistic regression (2003) Comput Stat Data Anal, 44, pp. 273-295 Härdle, W., Liang, H., Gao, J., (2000) Partially Linear Models, , Berlin: Springer He, X., Zhu, Z., Fung, W., Estimation in a semiparametric model for longitudinal data with unspecified dependence structure (2002) Biometrika, 89, pp. 579-590 Huber, P., (1981) Robust Statistics, , New York: Wiley Maronna, R., Martin, D., Yohai, V., (2006) Robust Statistics: Theory and Methods, , New York: Wiley Pierce, D., The asymptotic effect of substituting estimators for parameters in certain types of statistics (1982) Ann Stat, 10, pp. 475-478 Pollard, D., (1984) Convergence of Stochastic Processes, , New York: Springer Robins, J., Rotnitzky, A., Zhao, L., Estimation of regression coefficients when some regressors are not always observed (1994) J Am Stat Assoc, 89, pp. 846-866 Robins, J., Rotnitzky, A., Zhao, L., Analysis of semiparametric regression models for repeated outcomes in the presence of missing data (1995) J Am Stat Assoc, 90, pp. 106-121 Rosenbaum, P., Model-based direct adjustment (1987) J Am Stat Assoc, 82, pp. 387-394 Severini, T., Staniswalis, J., Quasi-likelihood estimation in semiparametric models (1994) J Am Stat Assoc, 89, pp. 501-511 van der Vaart, A., Wellner, J., (1996) Weak Convergence and Empirical Processes. With Applications to Statistics, , New York: Springer Wang, Q., Sun, Z., Estimation in partially linear models with missing responses at random (2007) J Multivar Anal, 98, pp. 1470-1493 Wang, C., Wang, S., Zhao, L., Ou, S., Weighted semiparametric estimation in regression analysis regression with missing covariates data (1997) J Am Stat Assoc, 92, pp. 512-525 Wang, C., Wang, S., Gutierrez, R., Carroll, R., Local linear regression for generalized linear models with missing data (1998) Ann Stat, 26, pp. 1028-1050 Wang, Q., Linton, O., Härdle, W., Semiparametric regression analysis with missing response at random (2004) J Am Stat Assoc, 99 (466), pp. 334-345 |
| ISSN: | 11330686 |
| DOI: | 10.1007/s11749-010-0216-0 |