Studies on Some Inferential Aspects of Graybill-Deal Estimators

This dissertation included two elds in the application of Statistical Inference, specialized in Meta Analysis and Estimation Theory viz. : `Estimation of Common Mean' and `function Estimation'. Part A Estimation of Common Mean. In Chapter 2, we extended Graybill-Deal Estimator (GDE) to the higher dimension: common parameter estimation in linear regression models. We found the same result continues to hold in situations wherein the p (p 2) linear regression models involve k (k > 1) common estimable parameter(s) in the mean models. In this context, we used the criterion of `Loewner Order Domination' of information or dispersion matrices. Then Chapter 3, we studied GDE's properties under Pitman closeness criterion. Specifically, we compared a p-source based Graybill-Deal estimator against its q-sub-source based competitors for q (< p)-dimensional subsets of p-dimensional data. Part B Function Estimation. In Chapter 4, we presented a negative report about the estimation of reliability function by using a single observation from a mixture of two exponential distributions. We showed that there exists proper estimator on if we require negative weight on the distributions. All the references cited in this thesis would be presented at the end.