Bal Debasmita, Tripathy Manas Ranjan, Kumar Somesh
Department of Mathematics, National Institute of Technology Rourkela, Rourkela, Odisha, India.
Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, India.
J Appl Stat. 2023 Sep 6;51(10):1976-2006. doi: 10.1080/02664763.2023.2251100. eCollection 2024.
The problems of point estimation and classification under the assumption that the training data follow a Lindley distribution are considered. Bayes estimators are derived for the parameter of the Lindley distribution applying the Markov chain Monte Carlo (MCMC), and Tierney and Kadane's [Tierney and Kadane, , J. Amer. Statist. Assoc. 81 (1986), pp. 82-86] methods. In the sequel, we prove that the Bayes estimators using Tierney and Kadane's approximation and Lindley's approximation both converge to the maximum likelihood estimator (MLE), as , where is the sample size. The performances of all the proposed estimators are compared with some of the existing ones using bias and mean squared error (MSE), numerically. It has been noticed from our simulation study that the proposed estimators perform better than some of the existing ones. Applying these estimators, we construct several plug-in type classification rules and a rule that uses the likelihood accordance function. The performances of each of the rules are numerically evaluated using the expected probability of misclassification (EPM). Two real-life examples related to disease are considered for illustrative purposes.
考虑在训练数据服从林德利分布的假设下的点估计和分类问题。应用马尔可夫链蒙特卡罗（MCMC）方法以及蒂尔尼和卡丹 [蒂尔尼和卡丹，《美国统计协会杂志》81（1986），第82 - 86页] 的方法，推导了林德利分布参数的贝叶斯估计量。接下来，我们证明使用蒂尔尼和卡丹近似以及林德利近似的贝叶斯估计量在样本量(n)趋于无穷时都收敛到最大似然估计量（MLE）。使用偏差和均方误差（MSE）对所有提出的估计量与一些现有估计量的性能进行了数值比较。从我们的模拟研究中注意到，所提出的估计量比一些现有估计量表现更好。应用这些估计量，我们构建了几个插件型分类规则以及一个使用似然符合函数的规则。使用误分类期望概率（EPM）对每个规则的性能进行了数值评估。为了说明目的，考虑了两个与[疾病名称未给出]疾病相关的实际例子。
