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Abstract:

In this paper, we consider the situation in which the observations follow an isotonic generalized partly linear model. Under this model, the mean of the responses is modelled, through a link function, linearly on some covariates and nonparametrically on an univariate regressor in such a way that the nonparametric component is assumed to be a monotone function. A class of robust estimates for the monotone nonparametric component and for the regression parameter, related to the linear one, is defined. The robust estimators are based on a spline approach combined with a score function which bounds large values of the deviance. As an application, we consider the isotonic partly linear log-Gamma regression model. Under regularity conditions, we derive consistency results for the nonparametric function estimators as well as consistency and asymptotic distribution results for the regression parameter estimators. Besides, the empirical influence function allows us to study the sensitivity of the estimators to anomalous observations. Through a Monte Carlo study, we investigate the performance of the proposed estimators under a partly linear log-Gamma regression model with increasing nonparametric component. The proposal is illustrated on a real data set. © 2019, Sociedad de Estadística e Investigación Operativa.

Registro:

Documento: Artículo
Título:Robust estimators in a generalized partly linear regression model under monotony constraints
Autor:Boente, G.; Rodriguez, D.; Vena, P.
Filiación:Departamento de Matemáticas, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and CONICET, Ciudad Universitaria, Pabellón 1, Buenos Aires, 1428, Argentina
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:B-splines; Deviance; Isotonic regression; Partial linear models; Robust estimation
Año:2019
DOI: http://dx.doi.org/10.1007/s11749-019-00629-7
Título revista:Test
Título revista abreviado:Test
ISSN:11330686
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_11330686_v_n_p_Boente

Referencias:

  • Aït Sahalia, Y., (1995) The Delta Method for Nonparametric Kernel Functionals, , Ph.D. dissertation, University of Chicago
  • Álvarez, E., Yohai, J., M -estimators for isotonic regression (2012) J Stat Plan Inference, 142, pp. 2241-2284
  • Bianco, A., Boente, G., Robust estimators in semiparametric partly linear regression models (2004) J Stat Plan Inference, 122, pp. 229-252
  • Bianco, A., Yohai, V., Robust estimation in the logistic regression model (1996) Lecture Notes in Statistics, 109, pp. 17-34. , Springer, New York
  • Bianco, A., García Ben, M., Yohai, V., Robust estimation for linear regression with asymmetric errors (2005) Can J Stat, 33, pp. 511-528
  • Bianco, A., Boente, G., Rodrigues, I., Resistant estimators in Poisson and Gamma models with missing responses and an application to outlier detection (2013) J Multivar Anal, 114, pp. 209-226
  • Bianco, A., Boente, G., Rodrigues, I., Robust tests in generalized linear models with missing responses (2013) Comput Stat Data Anal, 65, pp. 80-97
  • Birke, M., Dette, H., Testing strict monotonicity in nonparametric regression (2007) Math Methods Stat, 16, pp. 110-123
  • Boente, G., Rodríguez, D., Robust inference in generalized partially linear models (2010) Comput Stat Data Anal, 54, pp. 2942-2966
  • Boente, G., He, X., Zhou, J., Robust estimates in generalized partially linear models (2006) Ann Stat, 34, pp. 2856-2878
  • Boente, G., Rodríguez, D., Vena, P., (2018) Robust Estimators in a Generalized Partly Linear Regression Model under Monotony Constraints, , https://arxiv.org/abs/1802.07998
  • Cantoni, E., Ronchetti, E., Robust inference for generalized linear models (2001) J Am Stat Assoc, 96, pp. 1022-1030
  • Cantoni, E., Ronchetti, E., A robust approach for skewed and heavy tailed outcomes in the analysis of health care expenditures (2006) J Health Econ, 25, pp. 198-213
  • Croux, C., Haesbroeck, G., Implementing the Bianco and Yohai estimator for logistic regression (2002) Comput Stat Data Anal, 44, pp. 273-295
  • Du, J., Sun, Z., Xie, T., M -estimation for the partially linear regression model under monotonic constraints (2013) Stat Probab Lett, 83, pp. 1353-1363
  • Gijbels, I., Hall, P., Jones, M., Koch, I., Tests for monotonicity of a regression mean with guaranteed level (2000) Biometrika, 87, pp. 663-673
  • Härdle, W., Liang, H., Gao, J., (2000) Partially linear models, , Physica-Verlag, Wurzburg
  • He, X., Shi, P., Bivariate tensor-product B -spline in a partly linear model (1996) J Multivar Anal, 58, pp. 162-181
  • He, X., Shi, P., Monotone B-spline smoothing (1998) J Am Stat Assoc, 93, pp. 643-650
  • He, X., Zhu, Z., Fung, W., Estimation in a semiparametric model for longitudinal data with unspecified dependence structure (2002) Biometrika, 89, pp. 579-590
  • Heritier, S., Cantoni, E., Copt, S., Victoria-Feser, M.P., (2009) Robust methods in biostatistics. Wiley series in probability and statistics, , Wiley, New York
  • Huang, J., A note on estimating a partly linear model under monotonicity constraints (2002) J Stat Plan Inference, 107, pp. 343-351
  • Künsch, H., Stefanski, L., Carroll, R., Conditionally unbiased bounded influence estimation in general regression models with applications to generalized linear models (1989) J Am Stat Assoc, 84, pp. 460-466
  • Lu, M., Spline-based sieve maximum likelihood estimation in the partly linear model under monotonicity constraints (2010) J Multivar Anal, 101, pp. 2528-2542
  • Lu, M., Spline estimation of generalised monotonic regression (2015) J Nonparametr Stat, 27, pp. 19-39
  • Lu, M., Zhang, Y., Huang, J., Estimation of the mean function with panel count data using monotone polynomial splines (2007) Biometrika, 94, pp. 705-718
  • Mallows, C., (1974) On some topics in robustness, , Memorandum Bell Laboratories, Murray Hill
  • Manchester, L., Empirical influence for robust smoothing (1996) Aust J Stat, 38, pp. 275-296
  • Marazzi, A., Yohai, V., Adaptively truncated maximum likelihood regression with asymmetric errors (2004) J Stat Plan Inference, 122, pp. 271-291
  • Maronna, R., Martin, D., Yohai, V., (2006) Robust statistics: theory and methods, , Wiley, New York
  • McCullagh, P., Nelder, J., (1989) Generalized linear models, , 2, Champman and Hall, London
  • Ramsay, J., Monotone regression splines in action (1988) Stat Sci, 3, pp. 425-441
  • Schumaker, L., (1981) Spline functions: basic theory, , Wiley, New York
  • Schwarz, G., Estimating the dimension of a model (1978) Ann Stat, 6, pp. 461-464
  • Shen, X., Wong, W.H., Convergence rate of sieve estimates (1994) Ann Stat, 22, pp. 580-615
  • Stefanski, L., Carroll, R., Ruppert, D., Bounded score functions for generalized linear models (1986) Biometrika, 73, pp. 413-424
  • Stone, C.J., The dimensionality reduction principle for generalized additive models (1986) Ann Stat, 14, pp. 590-606
  • Sun, Z., Zhang, Z., Du, J., Semiparametric analysis of isotonic errors-in-variables regression models with missing response (2012) Commun Stat Theory Methods, 41, pp. 2034-2060
  • Tamine, J., (2002) Smoothed influence function: Another view at robust nonparametric regression, , Discussion paper 62 Sonderforschungsbereich 373, Humboldt-Universität zu Berlin
  • van der Geer, S., (2000) Empirical processes in M -estimation, , Cambridge University Press, Cambridge
  • van der Vaart, A., (1998) Asymptotic statistics. Cambridge series in statistical and probabilistic mathematics, , Cambridge University Press, Cambridge
  • van der Vaart, A., Wellner, J., (1996) Weak convergence and empirical processes. With applications to statistics, , Springer, New York
  • Wang, Y., Huang, J., Limiting distribution for monotone median regression (2002) J Stat Plann Infer, 108, pp. 281-287

Citas:

---------- APA ----------
Boente, G., Rodriguez, D. & Vena, P. (2019) . Robust estimators in a generalized partly linear regression model under monotony constraints. Test.
http://dx.doi.org/10.1007/s11749-019-00629-7
---------- CHICAGO ----------
Boente, G., Rodriguez, D., Vena, P. "Robust estimators in a generalized partly linear regression model under monotony constraints" . Test (2019).
http://dx.doi.org/10.1007/s11749-019-00629-7
---------- MLA ----------
Boente, G., Rodriguez, D., Vena, P. "Robust estimators in a generalized partly linear regression model under monotony constraints" . Test, 2019.
http://dx.doi.org/10.1007/s11749-019-00629-7
---------- VANCOUVER ----------
Boente, G., Rodriguez, D., Vena, P. Robust estimators in a generalized partly linear regression model under monotony constraints. Test. 2019.
http://dx.doi.org/10.1007/s11749-019-00629-7