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Robust median estimator in logistic regression. (English) Zbl 1146.62015
Summary: This paper introduces a median estimator of the logistic regression parameters. It is defined as the classical \(L_{1}\)-estimator applied to continuous data \(Z_{1},\dots ,Z_n\) obtained by statistical smoothing of the original binary logistic regression observations \(Y_{1},\dots ,Y_n\). 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.

MSC:
62F12 Asymptotic properties of parametric estimators
62F35 Robustness and adaptive procedures (parametric inference)
62J12 Generalized linear models (logistic models)
65C60 Computational problems in statistics (MSC2010)
Software:
minpack; robustbase
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