Mathematical Sciences: Investigations on Multivariate Statistical Decision Theory

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The project is intended to investigate the estimation of an unknown statistical covariance matrix of a multivariate random vector. It includes related charactertistics such as generalized variance, discriminant coefficients, correlation and precision matrices. The goal in the case of the normal distribution is to find admissible and minimax estimators and to determine prior distributions which give rise to such procedures. The asymptotic study of these problems is to be performed and the resulting problem of positive normal mean estimation will be studied in detail. The asymptotic distribution of the maximum spread for a sample from a bivariate normal distribution will be studied along with its asymptotic efficiency.