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.

摘要

重新讨论了分类为具有共同均值和有序方差的两个正态总体的问题。到目前为止，在文献中，作者已经提出了基于 Graybill-Deal 估计器或其改进版本的订单受限方差下的公共均值的分类规则。令人惊讶的是，共同平均值的最大似然估计 (MLE) 并未用于分类目的。然而，有趣的是，在大多数参数范围内，MLE 比 Graybill-Deal 估计器具有更好的性能。在本文中，利用 MLE 及其插件类型限制版本的公共均值，提出了两个新的分类规则。进一步得到了基于广义似然比检验方法的分类规则。而且，已经提出了一些基于顺序受限方差下的共同均值的改进的现有估计量的某些规则。更重要的是，已经进行了一项模拟研究，以数值方式比较所有分类规则（包括现有规则）的错误分类概率。已经观察到，与其他规则相比，基于 MLE 及其受限版本的分类规则表现得非常令人满意（如果不是最好的话）。