Point Estimation and Related Classification Problems for Several Lindley Populations with Application Using COVID-19 Data
JOURNAL OF APPLIED STATISTICS(2024)
Natl Inst Technol Rourkela | Indian Inst Technol Kharagpur
Abstract
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, Accurate approximations for posterior moments and marginal densities, 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 n -> infinity, where n 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 COVID-19 disease are considered for illustrative purposes.
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Key words
Approximate Bayes estimator,likelihood accordance classifier,Lindley's approximation,Markov chain Monte Carlo (MCMC) method,Tierney and Kadane's approximation,Bayesian plug-in classification rule,probability of misclassification
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