Estimating error rate of classification into several normal populations under equal mean restriction

Abstract

Classification of observation into several univariate normal populations is considered when the population means are unknown but equal. Plug-in Bayes classification rules based on different estimators of the common mean are proposed for k populations. When the variances are ordered, the rule based on the Graybill–Deal estimator is compared with another rule. We prove the consistency property of the classification rules. Confidence intervals of conditional error rate are derived for two and three populations. Under the assumption of ordered variances, Bayes estimator of the ratio of variances is derived to use as a plug-in estimator for classification. We derive estimators of the parameters of mixture densities associated with two normal populations with a common mean and propose classification rules for mixture distribution. An extensive simulation is performed to compare different rules and interval estimators of the conditional error rates.

Keywords:

• Bayes estimator
• Variance ratio
• Confidence interval
• Conditional error rate
• Probability of misclassification
• EM algorithm

AMS CLASSIFICATION:

• 62F30
• 62H30

Acknowledgments

The authors express sincere gratitude to the reviewers and Editor-in-Chief for their insightful remarks, which improved an earlier version of the manuscript.

Additional information

Funding

The research work of the first author is supported by a grant from the Science and Engineering Research Board, Govt. of India (Grant No. ECR/2017/000255).