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:

Highly robust and efficient estimators for generalized linear models with a dispersion parameter are proposed. The estimators are based on three steps. In the first step, the maximum rank correlation estimator is used to consistently estimate the slopes up to a scale factor. The scale factor, the intercept, and the dispersion parameter are robustly estimated using a simple regression model. Then, randomized quantile residuals based on the initial estimators are used to define a region S such that observations out of S are considered as outliers. Finally, a conditional maximum likelihood (CML) estimator given the observations in S is computed. We show that, under the model, S tends to the whole space for increasing sample size. Therefore, the CML estimator tends to the unconditional maximum likelihood estimator and this implies that this estimator is asymptotically fully efficient. Moreover, the CML estimator maintains the high degree of robustness of the initial one. The negative binomial regression case is studied in detail. © 2018, Sociedad de Estadística e Investigación Operativa.

Registro:

Documento: Artículo
Título:A robust conditional maximum likelihood estimator for generalized linear models with a dispersion parameter
Autor:Marazzi, A.; Valdora, M.; Yohai, V.; Amiguet, M.
Filiación:Institute of Social and Preventive Medicine, Lausanne, Switzerland
Nice Computing, Le Mont-sur-Lausanne, Switzerland
Departamento de matematicas and Instituto de cálculo, Facultad de ciencias exactas y naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
CONICET, Buenos Aires, Argentina
Palabras clave:Conditional maximum likelihood; Generalized linear model; Negative binomial regression; Overdispersion; Robust regression
Año:2019
Volumen:28
Número:1
Página de inicio:223
Página de fin:241
DOI: http://dx.doi.org/10.1007/s11749-018-0624-0
Título revista:Test
Título revista abreviado:Test
ISSN:11330686
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_11330686_v28_n1_p223_Marazzi

Referencias:

  • Abrevaya, J., Computation of the maximum rank correlation estimator (1999) Econ Lett, 62, pp. 279-285
  • Aeberhard, W.H., Cantoni, E., Heritier, S., Robust inference in the negative binomial regression model with an application to falls data (2014) Biometrics, 70, pp. 920-931
  • Agostinelli, C., Marazzi, A., (2018) Robustnegbin: Robust Estimates for the Negative Binomial Regression Model, , R package, Preliminary version
  • Alfons, A., (2015), ccaPP: (Robust) canonical correlation analysis via projection pursuit. R package version 0.3.1; Alfons, A., Croux, C., Filzmoser, P., Robust maximum association estimators (2017) J Am Stat Assoc, 112 (517), pp. 436-445
  • Amiguet, M., (2011) Adaptively Weighted Maximum Likelihood Estimation of Discrete Distributions, , Ph.D. thesis, Université de Lausanne, Switzerland
  • Austin, P.C., Rothwell, D.M., Tu, J.V., A comparison of statistical modeling strategies for analyzing length of stay after CABG surgery (2002) Health Serv Outcomes Res Methodol, 3, pp. 107-133
  • Cadigan, N.G., Chen, J., Properties of robust M-estimators for Poisson and negative binomial data (2001) J Stat Comput Simul, 70, pp. 273-288
  • Cantoni, E., Ronchetti, E., Robust inference for generalized linear models (2001) J Am Stat Assoc, 96 (455), pp. 1022-1030
  • Cantoni, E., Zedini, A., (2009) A robust version of the hurdle model, , Cahiers du département d’économétrie No 2009.07, Faculté des sciences économiques et sociales, Université de Genève
  • Carter, E.M., Potts, H.W.W., Predicting length of stay from an electronic patient record system: a primary total knee replacement example (2014) BMC Med Inform Decis Mak, 14, p. 26
  • Cuesta-Albertos, J.A., Matrán, C., Mayo-Iscar, A., Trimming and likelihood: robust location and dispersion estimate in the elliptical model (2008) Ann Stat, 36 (5), pp. 2284-2318
  • Davison, A.C., Snell, E.J., Residuals and diagnostics (1991) Statistical theory and modelling: in honour of Sir David Cox, pp. 83-106. , Hinkley DV, Reid N, Snell EJ, (eds), Chapman and Hall, Boca Raton
  • Dunn, P.K., Smyth, G.K., Randomized quantile residuals (1996) J Comput Graph Stat, 5 (3), pp. 236-244
  • Gervini, D., Yohai, V.J., A class of robust and fully efficient regression estimators (2002) Ann Stat, 30 (2), pp. 583-616
  • Ghosh, A., Basu, A., Robust estimation for independent non-homogeneous observations using density power divergence with applications to linear regression (2013) Electron J Stat, 7, pp. 2420-2456
  • Ghosh, A., Basu, A., Robust estimation in generalized linear models: the density power divergence approach (2016) TEST, 25, pp. 269-290
  • Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., Stahel, W.A., (1986) Robust statistics: the approach based on influence functions, , Wiley, New York
  • Han, A.K., Non-parametric analysis of a generalized regression model: the maximum rank correlation estimator (1987) J Econ, 35 (23), pp. 303-316
  • Han, A.K., A non-parametric analysis of transformations (1987) J Econ, 35 (2-3), pp. 191-209
  • Heritier, S., Cantoni, E., Copt, S., Victoria-Feser, M.P., (2009) Robust methods in biostatistics, , Wiley, Chichester
  • Hilbe, J.M., (2008) Negative binomial regression, , Cambridge University Press, Cambridge
  • Huber, P.J., (1980) Robust statistics, , Wiley, New York
  • Künsch, H.R., Stefanski, L.A., Carroll, R.J., Conditionally unbiased bounded-influence estimation in general regression models, with applications to generalized linear models (1989) J Am Stat Assoc, 84 (406), pp. 460-466
  • Locatelli, I., Marazzi, A., Yohai, V.J., Robust accelerated failure time regression (2010) Comput Stat Data Anal, 55 (1), pp. 874-887
  • Marazzi, A., Yohai, V.J., Adaptively truncated maximum likelihood regression with asymmetric errors (2004) J Stat Plan Inference, 122 (1-2), pp. 271-291
  • Marazzi, A., Yohai, V.J., Optimal robust estimates based on the Hellinger distance (2010) Adv Data Anal Classif, 4 (2), pp. 169-179
  • Marazzi, A., Paccaud, F., Ruffieux, C., Beguin, C., Fitting the distribution of length of stay by parametric models (1998) Med Care, 36 (6), pp. 915-927
  • Maronna, R.A., Martin, R.D., Yohai, V.J., (2006) Robust statistics theory and methods, , Wiley, New York
  • Min, Y., Agresti, A., Modeling nonnegative data with clumping at zero: a survey (2002) J Iran Stat Soc, 1 (1-2), pp. 7-33
  • Nelder, J.A., Wedderburn, R.W.M., Generalized linear models (1972) J R Stat Soc Ser A, 135 (3), pp. 370-384
  • Rousseeuw, P.J., Multivariate estimation with high breakdwon point (1985) Mathematical statistics and applications, pp. 283-297. , Grossman W, Pflug G, Vincze I, Wertz W, (eds), Reidel Publishing, Dordrecht
  • Sherman, R.P., The limiting distribution of the maximum rank correlation estimator (1993) Econometrica, 61 (1), pp. 123-137
  • Valdora, M., Yohai, V.J., Robust estimation in generalized linear models (2014) J Stat Plan Inference, 146, pp. 31-48
  • Yohai, V.J., High breakdown-point and high efficiency robust estimates for regression (1987) Ann Stat, 15 (2), pp. 642-656

Citas:

---------- APA ----------
Marazzi, A., Valdora, M., Yohai, V. & Amiguet, M. (2019) . A robust conditional maximum likelihood estimator for generalized linear models with a dispersion parameter. Test, 28(1), 223-241.
http://dx.doi.org/10.1007/s11749-018-0624-0
---------- CHICAGO ----------
Marazzi, A., Valdora, M., Yohai, V., Amiguet, M. "A robust conditional maximum likelihood estimator for generalized linear models with a dispersion parameter" . Test 28, no. 1 (2019) : 223-241.
http://dx.doi.org/10.1007/s11749-018-0624-0
---------- MLA ----------
Marazzi, A., Valdora, M., Yohai, V., Amiguet, M. "A robust conditional maximum likelihood estimator for generalized linear models with a dispersion parameter" . Test, vol. 28, no. 1, 2019, pp. 223-241.
http://dx.doi.org/10.1007/s11749-018-0624-0
---------- VANCOUVER ----------
Marazzi, A., Valdora, M., Yohai, V., Amiguet, M. A robust conditional maximum likelihood estimator for generalized linear models with a dispersion parameter. Test. 2019;28(1):223-241.
http://dx.doi.org/10.1007/s11749-018-0624-0