An investigation of sample influence functions for the ds estimate of the optimum error rate in discriminant analysis

Abstract

Approximate and exact influence functions are investigated for the Shrunken D or DS method of estimating the optimum error rate in a linear discriminant analysis with two populations. Two- and three-dimensional plots of these functions are constructed to illustrate regions where influential observations are most harmful. The extension of these results to higher dimensional cases are discussed. As expected, influence function values reveal that the impact of a perturbing point increases as sample size decreases. Influence function values are more extreme (higher and lower over the range of perturbed observations studied) when the Mahalanobis1 distance between the means are smaller. For sample sizes of 100 or less from each group, the exact expression for the inverted perturbed covariance matrix should be used when constructing the influence function.