Reference : Logistic discrimination using robust estimators: an influence function approach
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Logistic discrimination using robust estimators: an influence function approach
Croux, Christophe [> > > >]
Haesbroeck, Gentiane mailto [Université de Liège - ULg > Département de mathématique > Statistique (aspects théoriques) >]
Joossens, Kristel [> > > >]
Canadian Journal of Statistics = Revue Canadienne de Statistique
[en] classification ; diagnostic ; discrimination ; efficiency ; error rate ; influence function ; logistic regression ; robustness
[en] Logistic regression is frequently used for classifying observations into two groups. Unfortunately there are often outlying observations in a data set and these might affect the estimated model and the associated classification error rate. In this paper, the authors study the effect of observations in the training sample on the error rate by deriving influence functions. They obtain a general expression for the influence function of the error rate, and they compute it for the maximum likelihood estimator as well as for several robust logistic discrimination procedures. Besides being of interest in their own right, the influence functions are also used to derive asymptotic, classification efficiencies of different logistic discrimination rules. The authors also show how influential points can be detected by means of a diagnostic plot based on the values of the influence function.

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