Derivation and Application of In uence Function in Discriminant Analysis for Three Groups

Abstract

The influence function is used to develop criteria to detect outliers in discriminant analysis. We derive the influence function of observations that estimate the the misclassification probability in discriminant analysis for three groups. The proposed measures are applied to the facial image data to define outliers and redo the discriminant analysis excluding the outliers. The study proves that the derived influence function is more efficient than using the discriminant probability approach.

Graphical Methods for the Sensitivity Analysis in Discriminant Analysis

“…Using ideas from Cook (1977), the study of influential data points in discriminant analysis are used to investigate the effect on the estimated overall probability of misclassification if certain observations were deleted. Campbell (1978) considered the empirical influence curve, while Critchley and Vitiello (1991), Fung (1992Fung ( , 1995, Lahiff and Whitcomb (1990), Moreno-Roldán et al (2007) and Lee and Kim (2011) introduced relevant statistical measures based on Campbell (1978). Their papers are all based on the deletion principle.…”