Error-Rate Estimation in Discriminant Analysis

Estimating the Probability of Misclassifications in Two-Groups Discriminant Analysis

“…To answer this question, it is important to conduct some comparative studies, to compare the performances of those existing estimators. Some comparative studies, which comparing the performances of parametric and empirical (non-bootstrap) estimators, have been done by Lachenbruch and Mickey (1968), McLachlan (1974aMcLachlan ( , 1974bMcLachlan ( , 1974c, Snapinn and Knoke (1984), and Page (1985). The results of their studies can be summarized as follows.…”

“…Many investigators found that this estimator is optimistically biased for estimating the actual error rate, particularly when the training samples are small (see for example, Dunn and Varady (1966), and Hills (1966)). The other parametric estimators denoted by DS, O, OS, L, and M are modifications (improvements) of the D-estimator with various bias reduction terms, proposed and compared by Okamoto (1963), Lachenbruch (1968), Lachenbruch and Mickey (1968), McLachlan (1974a), Page (1985), Ganeshanandam and Krzanowski (1990), and some others. Some authors also proposed smoothed estimators as bias corrections to D and DS estimators (see Glick (1978), Snapinn (1983), Snapinn and Knoke (1985)).…”