Alternative classification rules for two normal populations with a common mean and ordered variances

Abstract

The problem of classification into two normal populations with a common mean and ordered variances is revisited. So far in the literature, authors have proposed classification rules which are based on either the Graybill-Deal estimator or its improved version of the common mean under order restricted variances. Surprisingly, the maximum likelihood estimator (MLE) of the common mean has not been used for classification purposes. However, it is interesting to know that the MLE has better performance than the Graybill-Deal estimator in most of the parameter ranges. In this article, utilizing the MLE and its plug-in type restricted version of the common mean, two new classification rules have been proposed. Further, a classification rule based on the generalized likelihood ratio test approach has been obtained. Moreover, certain rules based on some of the improved existing estimators of the common mean under order restricted variances have been proposed. More importantly, a simulation study has been carried out to numerically compare the probabilities of misclassification for all the classification rules, including the existing ones. It has been observed that the classification rules which are based on the MLE and its restricted version perform quite satisfactorily (if not the best) compared to other rules.