Kumar Pushkal, Tripathy Manas Ranjan, Kumar Somesh
Department of Mathematics, National Institute of Technology Rourkela, Rourkela, India.
Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, India.
J Appl Stat. 2022 Oct 15;51(3):407-429. doi: 10.1080/02664763.2022.2129044. eCollection 2024.
The problem of classification into two inverse Gaussian populations with a common mean and ordered scale-like parameters is considered. Surprisingly, the maximum likelihood estimators (MLEs) of the associated model parameters have not been utilized for classification purposes. Note that the MLEs of the model parameters, including the MLE of the common mean, do not have closed-form expressions. In this paper, several classification rules are proposed that use the MLEs and some plug-in type estimators under order restricted scale-like parameters. In the sequel, the risk values of all the proposed estimators are compared numerically, which shows that the proposed plug-in type restricted MLE performs better than others, including the Graybill-Deal type estimator of the common mean. Further, the proposed classification rules are compared in terms of the expected probability of correct classification (EPC) numerically. It is seen that some of our proposed rules have better performance than the existing ones in most of the parameter space. Two real-life examples are considered for application purposes.
考虑了将具有共同均值和有序尺度参数的两个逆高斯总体进行分类的问题。令人惊讶的是，相关模型参数的最大似然估计（MLE）尚未用于分类目的。请注意，模型参数的MLE，包括共同均值的MLE，没有闭式表达式。本文提出了几种分类规则，这些规则在有序受限尺度参数下使用MLE和一些插件型估计器。随后，对所有提出的估计器的风险值进行了数值比较，结果表明，所提出的插件型受限MLE比其他估计器表现更好，包括共同均值的Graybill-Deal型估计器。此外，还对提出的分类规则在正确分类的期望概率（EPC）方面进行了数值比较。可以看出，我们提出的一些规则在大多数参数空间中比现有规则具有更好的性能。为了应用目的，考虑了两个实际例子。
