Influence of observations on the misclassification probability in quadratic discriminant analysis

Authors:
Christophe Croux;Kristel Joossens
Affiliations:
Department of Applied Economics, Katholieke Universiteit Leuven, Naamsestraat 69, B-3000 Leuven, Belgium;Department of Applied Economics, Katholieke Universiteit Leuven, Naamsestraat 69, B-3000 Leuven, Belgium
Venue:
Journal of Multivariate Analysis
Year:
2005

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Abstract

In this paper it is studied how observations in the training sample affect the misclassification probability of a quadratic discriminant rule. An approach based on partial influence functions is followed. It allows to quantify the effect of observations in the training sample on the performance of the associated classification rule. Focus is on the effect of outliers on the misclassification rate, merely than on the estimates of the parameters of the quadratic discriminant rule. The expression for the partial influence function is then used to construct a diagnostic tool for detecting influential observations. Applications on real data sets are provided.