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:

We introduce a new class of robust estimators for generalized linear models which is an extension of the class of projection estimators for linear regression. These projection estimators are defined using an initial robust estimator for a generalized linear model with only one unknown parameter. We found a bound for the maximum asymptotic bias of the projection estimator caused by a fraction ε of outlier contamination. For small ε, this bias is approximately twice the maximum bias of the initial estimator independently of the number of regressors. Since these projection estimators are not asymptotically normal, we define one-step weighted M-estimators starting at the projection estimators. These estimators have the same asymptotic normal distribution as the M-estimator and a degree of robustness close to the one of the projection estimator. We perform a Monte Carlo simulation for the case of binomial and Poisson regression with canonical links. This study shows that the proposed estimators compare favorably with respect to other robust estimators. Supplemental Material containing the proofs and the numerical algorithm used to compute the P-estimator is available online. © 2011 American Statistical Association.

Registro:

Documento: Artículo
Título:Projection estimators for generalized linear models
Autor:Bergesio, A.; Yohai, V.J.
Filiación:Universidad Nacional del Litoral, IMAL, Güemes 3450, S3000GLN Santa Fe, Argentina
Departamento de Matemáticas, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón 1, 1428 Buenos Aires, Argentina
Palabras clave:Logistic regression; Maximum bias; One-step estimators; Robust estimators
Año:2011
Volumen:106
Número:494
Página de inicio:661
Página de fin:671
DOI: http://dx.doi.org/10.1198/jasa.2011.tm09774
Título revista:Journal of the American Statistical Association
Título revista abreviado:J. Am. Stat. Assoc.
ISSN:01621459
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01621459_v106_n494_p661_Bergesio

Referencias:

  • Bianco, A., Yohai, V.J., Robust estimation in the logistic regression model (1996) Robust Statistics, Data Analysis and Computer Intensive Methods, Proceedings of the Workshop in Honor of Peter Huber. Lecture Notes in Statistics, 109, pp. 7-34. , H. Rieder, New York: Springer-Verlag, [661,666]
  • Bondell, H.D., Minimum distance estimation for the logistic regression model (2005) Biometrika, 92, pp. 724-731. , [661]
  • Cantoni, E., Ronchetti, E., Robust inference for generalized linear models (2001) Journal of the American Statistical Association, 96, pp. 1022-1030. , [661,669]
  • Carroll, R.J., Pederson, S., On robustness in the logistic regression model (1993) Journal of the Royal Statistical Society, Ser. B, 55, pp. 693-706. , [661]
  • Christmann, A., Least median of weighted squares in logistic regression with large strata (1994) Biometrika, 81, pp. 413-417. , [661]
  • Čížek, P., Robust and efficient adaptive estimation of binary-choice regression models (2008) Journal of the American Statistical Association, 103, pp. 687-696. , [661,667]
  • Copas, J.B., Binary regression models for contamination data (1988) Journal of the Royal Statistical Society, Ser. B, 50, pp. 225-265. , [661]
  • Croux, C., Haesbroeck, G., Implementing the bianco and yohai estimator for logistic regression (2003) Computational Statistics and Data Analysis, 44, pp. 273-295. , [661]
  • Croux, C., Flandre, C., Haesbroeck, G., The breakdown behavior of the maximum likelihood estimator in the logistic regression model (2002) Statistics and Probability Letters, 60, pp. 377-386. , [661,665-667]
  • García, B.M., Yohai, V.J., Quantile-Quantile plot for deviance residuals in the generalized linear model (2004) Journal of Computational and Graphical Statistics, 13, pp. 36-47. , [671]
  • Gervini, D., Robust adaptive estimators for binary regression models (2005) Journal of Statistical Planning and Inference, 131, pp. 297-311. , [661]
  • Kordzakhia, N., Mishra, G.D., Reiersølmoen, L., Robust estimation in the logistic regression model (2001) Journal of Statistical Planning and Inference, 98, pp. 211-223. , [661]
  • Künsch, H., Stefanski, L., Carroll, R., Conditionally unbiased bounded-influence estimation in general regression models, with applications to generalized linear models (1989) Journal of the American Statistical Association, 84, pp. 460-466. , [661,664,669,670]
  • Maronna, R.A., Yohai, V.J., Bias-Robust estimates of regression based on projections (1993) The Annals of Statistics, 21, pp. 965-990. , [661,663]
  • Maronna, R.A., Bustos, O., Yohai, V.J., Bias and efficiency robustness of general m-estimators for regression with random carriers (1979) Smoothing Techniques for Curve Estimation. Lectures Notes in Mathematics, 757, pp. 91-111. , T. Gasser and M. Rosenblatt, New York: Springer Verlag, [661]
  • Maronna, R.A., Martin, R.D., Yohai, V.J., (2006) Robust Statistics: Theory and Methods, , Chichister: Wiley. [662,665]
  • Maronna, R.A., Robust-Bias estimates for multivariate scatter based on projections (1992) Journal of Multivariate Analysis, 42, pp. 141-163. , [661]
  • Martin, R.A., Yohai, V.J., Zamar, R.H., Min-Max bias robust regression (1989) The Annals of Statistics, 17, pp. 1608-1630. , [663]
  • Müller, C.H., Neykov, N.M., Breakdown points of trimmed likelihood estimators and related estimators in generalized linear models (2003) Journal of Statistical Planning and Inference, 116, pp. 503-519. , [661]
  • Pregibon, D., Logistic regression diagnostics (1981) The Annals of Statistics, 9, pp. 705-724. , [661]
  • Rousseeuw, P., Leroy, A., (1987) Robust Regression and Outlier Detection, , New York: Wiley.[667]
  • Simpson, D.G., Ruppert, D., Carroll, R.J., On one-step gm estimates and stability of inferences in linear regression (1992) Journal of the American Statistical Association, 87, pp. 439-450. , [666]
  • Stefanski, L.A., Carroll, R.J., Ruppert, D., Optimally bounded score functions for generalized linear models with applications to logistic regression (1986) Biometrika, 73, pp. 413-424. , [670]
  • Tyler, D.E., Finite sample breakdown points of projection based multivariate location and scatter statistics (1994) The Annals of Statistics, 22, pp. 1024-1044. , [661]
  • Wedderburn, R.W.M., Quasi-Likelihood functions, generalized linear models, and the gauss-newton method (1974) Biometrika, 61, pp. 439-447. , [661]
  • Zuo, Y., Projection based depth functions and associated medians (2003) The Annals of Statistics, 31, pp. 1460-1490. , [663]

Citas:

---------- APA ----------
Bergesio, A. & Yohai, V.J. (2011) . Projection estimators for generalized linear models. Journal of the American Statistical Association, 106(494), 661-671.
http://dx.doi.org/10.1198/jasa.2011.tm09774
---------- CHICAGO ----------
Bergesio, A., Yohai, V.J. "Projection estimators for generalized linear models" . Journal of the American Statistical Association 106, no. 494 (2011) : 661-671.
http://dx.doi.org/10.1198/jasa.2011.tm09774
---------- MLA ----------
Bergesio, A., Yohai, V.J. "Projection estimators for generalized linear models" . Journal of the American Statistical Association, vol. 106, no. 494, 2011, pp. 661-671.
http://dx.doi.org/10.1198/jasa.2011.tm09774
---------- VANCOUVER ----------
Bergesio, A., Yohai, V.J. Projection estimators for generalized linear models. J. Am. Stat. Assoc. 2011;106(494):661-671.
http://dx.doi.org/10.1198/jasa.2011.tm09774