In this paper we consider of location parameter estimation in the multivariate normal distribution with unknown covariance. Two restrictions on the mean vector parameter are imposed. First we assume that all elements of mean vector are nonnegative, at the second hand assumed only a subset of elements are nonnegative. We propose a class of shrinkage estimators which dominate the minimax estimator of mean vector under the quadratic loss function.

In this paper, the wavelet estimators of the nonparametric regression function based on the various thresholds under the mixture prior distribution and the mean square error loss function in Bosove space are computed. Also, using a simulation study the optimality of different wavelet thresholding estimators such as posterior mean, posterior median, Bayes factor, universal threshold and sure threshold are investigated. The results show that the average mean square error of sure threshold estimator is less than the other obtained estimators.