Mathematical Sciences: Topics in Decision Theory and Multivariate Analysis

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The research is concentrated in the areas of admissibility of decision rules obtained from improper prior distributions, asymptotic distribution theory for singular values of random matrices, and concentration inequalities with applications in linear models. The evaluation and comparison of decision rules obtained from improper prior distributions is the goal of the research on admissibility. A technique will be developed to find the asymptotic distribution of singular values of random matrices which is similar to a recently developed technique for finding the asymptotic distribution of the eigenvalues of symmetric random matrices. Concentration inequalities are an important tool in obtaining bounds on the operating characteristics of some statistical procedures. New concentration inequalities will be developed which may be applied in linear models.