Bayesian estimation for mean vector of multivariate normal distribution on the linear and nonlinear exponential balanced loss based on wavelet decomposition

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 the soft shrinkage wavelet estimators was 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 nonlinear 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.