The 95% confidence intervals of error rates and discriminant coefficients
Shuichi Shinmura · Statistics Optimization & Information Computing · 2015
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.