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Hobza, Pavel and Pardo Llorente, Leandro and Vajda, Igor
(2008)
*Robust median estimator in logistic regression.*
Journal of Statistical Planning and Inference, 138
(12).
pp. 3822-3840.
ISSN 0378-3758

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Official URL: http://www.sciencedirect.com/science/article/pii/S0378375808001407

## 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.

Item Type: | Article |
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Uncontrolled Keywords: | logistic regression; MLE; Morgenthaler estimator; Bianco and Yohai estimator; Croux and Haselbroeck estimator; median estimator; consistency; asymptotic normality; robustness;Generalized linear-models; Nonlinear-regression; Fits |

Subjects: | Sciences > Mathematics > Applied statistics Sciences > Mathematics > Mathematical statistics |

ID Code: | 17513 |

Deposited On: | 20 Dec 2012 11:08 |

Last Modified: | 26 Jul 2018 10:56 |

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