Mahmoud Afshari

This paper addresses the problem of bayesian wavelet estimating the mean vector of multivariate normal distribution under a multivariate normal prior distribution based on linear and nonlinear exponential balanced loss functions. The covariance matrix of multivariate normal distribution is considered known. Bayes estimators of mean vector parameter of multivariate normal distribution are achieved. Then two soft shrinkage wavelet threshold estimators based on Stein's unbiased risk estimate ($SURE$) and bayes estimators are provided. Finally the performance of soft shrinkage wavelet estimator checked through simulation study and Electrical Grid Stability Simulated data set. Simulation and real data results showed the better performance of $SURE$ thresholds based on linear and nolinear exponential balanced loss functions compared to other classical wavelet methods. Also they showed better performance for $SURE$ threshold based on nonlinear exponential balanced loss function in multivariate normal distribution with small dimensions. \end{abstract}