Mathematical Sciences: Prediction Theory, Asymptotic Distributions of Eigenvalues, Confidence Set Validity

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The research project consists of three problems. The first deals with prediction theory and improper priors. The goal is to find usable inferential procedures starting from improper priors, which will have certain optimal properties. The second problem will find asymptotic distribution of eigenvalues of random symmetric matrices. The third problem is that of construction of confidence intervals for linear functions of regression parameters. Such confidence intervals are found by asymptotic arguments and hence computable tight upper and lower bounds are hard to find. The principal investigator will develop such bounds.