Date of Award


Degree Type


Degree Name

Doctor of Philosophy


The classical theory of Multivariate Statistical Analysis is primarily based on the multivariate normal model. However, in the recent literature several authors have made studies as to how the conclusions will be affected if the population model departs from normality. The class of elliptical models shares some intrinsic properties of the multivariate normal model and has been getting increasing attention by the researchers in the recent literature.;In the present thesis we restrict the model to a suitable multivariate t-model which belongs to the class of elliptical models and at the same time accommodates the multivariate normal model. This model has found applications in the context of stock market problems. The main results of the thesis are outlined below.;Improved estimators of the scale matrix of the multivariate t-model have been obtained under a squared error loss function. Similar improved estimators for the characteristic roots of the scale matrix, trace of the scale matrix and also for the inverse of the scale matrix have been obtained. Some Improved estimators of the scale matrix of multivariate t-model have been obtained under the entropy loss function. Some other related new results are as follows.;An elegant expression has been obtained for the characteristic function of the multivariate t-distribution in terms of the well-known Macdonald function. Also a limit theory for the Macdonald function has been obtained. Some identities involving expectations of the sum of product matrix, based on the multivariate t-model, have been derived.



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