Geodesic
Robust median estimator for generalized linear models with binary responses
Kybernetika, Tome 48 (2012) no. 4, pp. 768-794

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The paper investigates generalized linear models (GLM's) with binary responses such as the logistic, probit, log-log, complementary log-log, scobit and power logit models. It introduces a median estimator of the underlying structural parameters of these models based on statistically smoothed binary responses. Consistency and asymptotic normality of this estimator are proved. Examples of derivation of the asymptotic covariance matrix under the above mentioned models are presented. Finally some comments concerning a method called enhancement and robustness of median estimator are given and results of simulation experiment comparing behavior of median estimator with other robust estimators for GLM's known from the literature are reported.
Classification : 62F10, 62F12, 62F35
Keywords: generalized linear models; binary responses; statistical smoothing; statistical enhancing; maximum likelihood estimator; median estimator; consistency; asymptotic normality; efficiency; robustness 
@article{KYB_2012__48_4_a7,
     author = {Hobza, Tom\'a\v{s} and Pardo, Leandro and Vajda, Igor},
     title = {Robust median estimator for generalized linear models with binary responses},
     journal = {Kybernetika},
     pages = {768--794},
     publisher = {mathdoc},
     volume = {48},
     number = {4},
     year = {2012},
     mrnumber = {3013398},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012__48_4_a7/}
}
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Hobza, Tomáš; Pardo, Leandro; Vajda, Igor. Robust median estimator for generalized linear models with binary responses. Kybernetika, Tome 48 (2012) no. 4, pp. 768-794. http://geodesic.mathdoc.fr/item/KYB_2012__48_4_a7/