Abstract
Fisher proposed a linear discriminant function (Fisher’s LDF). From 1971, we analysed electrocardiogram (ECG) data in order to develop the diagnostic logic between normal and abnormal symptoms by Fisher’s LDF and a quadratic discriminant function (QDF). Our four years research was inferior to the decision tree logic developed by the medical doctor. After this experience, we discriminated many data and found four problems of the discriminant analysis. A revised Optimal LDF by Integer Programming (Revised IP-OLDF) based on the minimum number of misclassification (minimum NM) criterion resolves three problems entirely [13, 18]. In this research, we discuss fourth problem of the discriminant analysis. There are no standard errors (SEs) of the error rate and discriminant coefficient. We propose a k-fold crossvalidation method. This method offers a model selection technique and a 95% confidence intervals (C.I.) of error rates and discriminant coefficients.
Highlights
Fisher [3] described the linear discriminant function (Fisher’s Linear Discriminant Function (LDF)) and founded the discriminant theory
We showed that the means of error rates (M1) in the training sample and M2 of Revised IP-Optimal Linear Discriminant Functions (OLDFs) were less than those of Fisher’s LDF[20]
We have discussed the fourth problem of discriminant analysis
Summary
Fisher [3] described the linear discriminant function (Fisher’s LDF) and founded the discriminant theory. Konishi and Honda [6] proposed the “bootstrap methods [1] for error rate estimation in discriminant analysis”, a new approach is more helpful for researchers who wish to discriminate their small sample. In addition to these results, we discuss the new model selection technique. Some statisticians believe MNM is foolish criterion because it overfits the training sample and overestimates the validation sample They say the generalization ability of Fisher’s LDF is good because it assumes the Fisher’s assumption without examination of real data. It can resolve fourth problem of the discriminant analysis
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
