Seminar Title
Estimation and Classification Problems under Equality Restrictions on Parameters
Seminar Type
Synopsis Seminar
Speaker Name
Pushkal Kumar ( Rollno : 518ma1002)
Speaker Type
Seminar Room (Department of Mathematics)
Date & Time
24 Mar 2023 11.15 AM
Prof. Manas Ranjan Tripathy

The problems of estimation and classification under the equality restriction on model parameters are well-known in the statistical inference and classification literature. The underlying problem has a wide range of applications in various fields of study, including medical diagnosis, pattern recognition, military surveillance, finance, social science etc. In this thesis, we focus on estimating model parameters under equality restriction for some well-known probabilistic models and then utilize these estimators to construct classification rules, studying their misclassification error rates and accuracy. Notably, we consider the estimation and classification problems for normal, inverse Gaussian, logistic and exponential populations under equality restrictions on the location parameters. In the sequel, we derive some new estimators for the model parameters using standard techniques, such as the Brewster-Zidek method, the MCMC method, and the Rao-Blackwell method. These improved estimators and their original counterparts are utilized to construct classification rules under the same probabilistic model setup to classify a new observation or a group of observations into one of these populations. The oracle property for some of the rules has been proved. In some cases, we derive the theoretical comparison of individual probabilities of misclassification and correct classification. In each case, a detailed numerical comparison of all the estimators and the corresponding classification rules are compared. The estimators are compared in terms of bias, mean squared error and risk values. In contrast, the classification rules are compared using the individual probabilities of misclassification, expected probability, and the expected probability of correct classification. The theoretical findings are well supported by some real-life data analysis which shows the potential application of our proposed model problem.