Mahmoud Afshari

The expression of the characteristics of many phenomena in the real world is affected by several variables or characteristics. Therefore, we are faced with phenomena that, based on their inherent characteristics, a random vector or matrix is used to represent them. In other words, it can be said that these phenomena follow multivariate or matrix-variate distributions. In 1956, Stein showed that the sample mean is the inadmissible estimator of mean vector of the multivariate normal distribution with dimension 3 and more. After the presentation of Stein's phenomenon, many efforts were made to achieve an optimal estimator of the location parameter vector in dimensions 3 and higher in the multivariate normal distribution and other multivariate distributions. In this thesis, the point estimation of the location parameter of multivariate and matrix-variate distributions have been investigated. In multivariate distributions, location vector estimation with Bayesian wavelet approach in the family of elliptic distributions based on nonlinear exponential balanced loss function has been studied and researched. Also, the estimation of the location matrix of the matrix variate normal distributions based on the Bayesian wavelet method and the two prior distributions: normal matrix variate and improper prior distribution has been investigated. First, by using the Bayes technique and the balanced loss function, the Bayes or generalized Bayes estimator was introduced based on the desired prior distribution, and the admissibility and minimaxity of these estimators were checked. Then using the methods of determining the wavelet risk threshold of Stein and Huang based on Bayes and generalized Bayes estimators, Bayesian wavelet estimators were introduced. At the end, the accuracy of the theoretically proposed estimators has been investigated with the help of simulation study and real examples.