The influence of observations for local log-odd in linear discriminant analysis

In discriminant analysis, it is often the observations that are difficult to classify that arouse our attention most. We propose diagnostic measures that are defined locally for those observations lying adjacent to the discriminant plane. Different constant values of the discriminant rule have been tried for the proposed measures. These measures are expressed in terms of two fundamental diagnostic statistics in discriminant analysis, proposed independently by Critchley and Vitiello (1991) and Fung (1992). They can be compared using contour plots with other measures such as the Johnson (1987) type measures that are defined over the whole discriminant space. The proposed measures, when studied with simulated confidence envelopes, are found to be useful for detecting influential observations.