On the sensitivity of linear discriminant analysis to sampling variation and analytical errors.

The influence of analytical inaccuracy and imprecision on the linear discriminant function is considered. Analytical shifts occurring between the analysis of samples from each of two groups give spuriously low error rates if the function is evaluated on the training set, notably at high dimensions. Inaccuracy arising after the establishment of a discriminant function may change considerably the individual group error rates whereas the overall error rate is moderately affected. Imprecision decreases the group separation by an amount comparable to that in the univariate situation. In conclusion, evaluation of the error rates of a discriminant function on an independent test set is important to obtain realistic estimates of the performance and is preferable to using unbiased statistical methods or the split-sample principle based solely upon the training set.