Robust median estimator in logistic regression
| dc.contributor.author | Hobza, Pavel | |
| dc.contributor.author | Pardo Llorente, Leandro | |
| dc.contributor.author | Vajda, Igor | |
| dc.date.accessioned | 2023-06-20T09:43:19Z | |
| dc.date.available | 2023-06-20T09:43:19Z | |
| dc.date.issued | 2008-12-01 | |
| dc.description.abstract | This paper introduces a median estimator of the logistic regression parameters. It is defined as the classical L-1-estimator applied to continuous data Z(1),..., Z(n) obtained by a statistical smoothing of the original binary logistic regression observations Y-1,..., Y-n. Consistency and asymptotic normality of this estimator are proved. A method called enhancement is introduced which in some cases increases the efficiency of this estimator. Sensitivity to contaminations and leverage points is studied by simulations and compared in this manner with the sensitivity of some robust estimators previously introduced to the logistic regression. The new estimator appears to be more robust for larger sample sizes and higher levels of contamination. | |
| dc.description.department | Depto. de Estadística e Investigación Operativa | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17513 | |
| dc.identifier.doi | 10.1016/j.jspi.2008.02.010 | |
| dc.identifier.issn | 0378-3758 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0378375808001407 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50246 | |
| dc.issue.number | 12 | |
| dc.journal.title | Journal of Statistical Planning and Inference | |
| dc.language.iso | eng | |
| dc.page.final | 3840 | |
| dc.page.initial | 3822 | |
| dc.publisher | Elsevier Science Bv | |
| dc.relation.projectID | MTM 2006-06872 | |
| dc.relation.projectID | MSMT 1M 0572 | |
| dc.relation.projectID | MPO FI-IM3/136 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 519.233.5 | |
| dc.subject.keyword | logistic regression | |
| dc.subject.keyword | MLE | |
| dc.subject.keyword | Morgenthaler estimator | |
| dc.subject.keyword | Bianco and Yohai estimator | |
| dc.subject.keyword | Croux and Haselbroeck estimator | |
| dc.subject.keyword | median estimator | |
| dc.subject.keyword | consistency | |
| dc.subject.keyword | asymptotic normality | |
| dc.subject.keyword | robustness | |
| dc.subject.keyword | Generalized linear-models | |
| dc.subject.keyword | Nonlinear-regression | |
| dc.subject.keyword | Fits | |
| dc.subject.ucm | Estadística aplicada | |
| dc.subject.ucm | Estadística matemática (Matemáticas) | |
| dc.subject.unesco | 1209 Estadística | |
| dc.title | Robust median estimator in logistic regression | |
| dc.type | journal article | |
| dc.volume.number | 138 | |
| dcterms.references | Adimari, G., Ventura, L., 2001. Robust inference for generalized linear models with application to logistic regression. Statist. Probab. Lett. 55 (4), 413--419. Agresti, A., 2002. Categorical Data Analysis. second ed. Wiley, New York. Andersen, E.B., 1990. The Statistical Analysis of Categorical data. Springer, New York. Arcones, M.A., 2001. Asymptotic distribution of regression M-estimators. J. Statist. Plann. Inference 97, 235--261. Bianco, A.M., Yohai, V.J., 1996. Robust estimation in the logistic regression model. In: Robust Statistics, Data Analysis, and Computer Intensive Methods (Schloss Thurnau, 1994). Lecture Notes in Statistics, vol. 109, Springer, New York, pp. 17--34. Chen, X.R., Zhao, L., Wu, Y., 1993. On conditions of consistency of ML1N estimates. Statist. Sinica 3, 9--18. Croux, C., Haesbroeck, G., 2003. Implementing the Bianco and Yohai estimator for logistic regression. Comput. Statist. Data Anal. 44, 273--295. Dennis Jr., J.E., Schnabel, R.B., 1983. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Englewood Cliffs, NJ. Gervini, D., 2005. Robust adaptive estimators for binary regression models. J. Statist. Plann. Inference 131, 297--311. Hampel, F.R., Rousseeuw, P.J., Ronchetti, E.M., Stahel, W.A., 1986. Robust Statistics: The Approach Based on Influence Functions. Wiley, New York. Hobza, T., Pardo, L., Vajda, I., 2005. Median estimators in generalized logistic regression. Research Report DAR-UTIA 2005/40, Institute of Information Theory, Prague (available at http://dar.site.cas.cz/?publication = 1007). Hobza, T., Pardo, L., Vajda, I., 2006. Robust median estimators in logistic regression. Research Report DAR-UTIA 2006/31, Institute of Information Theory, Prague (available at http://dar.site.cas.cz/?publication = 1089). Jurečková, J., Proch´azka, B., 1994. Regression quantiles and trimmed least squares estimator in nonlinear regression model. Nonparametric Statist. 3, 201--222. Jurečková, J., Sen, P.K., 1996. Robust Statistical Procedures. Wiley, New York. Knight, K., 1998. Limiting distributions for L1 regression estimators under general conditions. Ann. Statist. 26, 755--770. Koenker, R., Basset, G., 1978. Regression quantiles. Econometrica 46, 33--50. Kordzakhia, N., Mishra, G.D., ReiersZlmoen, L., 2001. Robust estimation in the logistic regression model. J. Statist. Plann. Inference 98, 211--223. Liese, F., Vajda, I., 1999. M-estimators of structural parameters in pseudolinear models. Appl. Math. 44, 245--270. Liese, F., Vajda, I., 2003. A general asymptotic theory of M-estimators I. Math. Methods Statist. 12, 454--477. Liese, F., Vajda, I., 2004. A general asymptotic theory of M-estimators II. Math. Methods Statist. 13, 82--95. Maronna, R.A., Martin, R.D., Yohai, V.J., 2006. Robust Statistics. Theory and Methods. Wiley, New York. Mood, A.M., Graybill, F.A., Boes, D.C., 1974. Introduction to the Theory of Statistics. McGraw-Hill, New York. Moré, J., Burton, G., Kenneth, H., 1980. User Guide for MINPACK-1. Argonne National Laboratory Report ANL-80-74, Argonne, Illinois. Morgenthaler, S., 1992. Least-absolute-deviations fits for generalized linear models. Biometrika 79, 747--754. Pardo, J.A., Pardo, L., Pardo, M.C., 2006. Testing in logistic regression models based on -divergences measures. J. Statist. Plann. Inference 136, 982--1006. Pollard, D., 1991. Asymptotics for least absolute deviation regression estimators. Econometric Theory 7, 186--199. Pregibon, D., 1982. Resistant fits for some commonly used logistic models with medical applications. Biometrics 38, 485--498. Richardson, G.D., Bhattacharyya, B.B., 1987. Consistent L1-estimates in nonlinear regression for a noncompact parameter space. Sankhya Ser. A 49, 377--387. Rousseeuw, P.J., Christmann, A., 2003. Robustness against separation and outliers in logistic regression. Comput. Statist. Data Anal. 43, 315--332. Yohai, V.J., 1987. High breakdown point high efficiency robust estimates for regression. Ann. Statist. 15, 642--656. Zwanzig, S., 1997. On L1-norm Estimators in Nonlinear Regression and in Nonlinear Error-in-Variables Models. IMS Lecture Notes, vol. 31, Hayward, pp. 101--118. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | a6409cba-03ce-4c3b-af08-e673b7b2bf58 | |
| relation.isAuthorOfPublication.latestForDiscovery | a6409cba-03ce-4c3b-af08-e673b7b2bf58 |
Download
Original bundle
1 - 1 of 1