Location parameter estimation for elliptical distribution under the balanced-LINEX loss

Location parameter estimation is an important problem in the point estimation for multivariate distribution. In this paper, for an elliptical family of distributions with unknown location vector and known scale matrix, a wavelet shrinkage procedure for point estimating the unknown location vector is suggested. We find the shrinkage soft threshold estimator based on Stein’s unbiased risk estimate (SURE) threshold under the balanced-LINEX loss function. In addition, we obtain the restricted shrinkage soft threshold estimator based on non-negative sub vector of the location vector. Finally, through a simulation study, we investigate the behavior of the proposed estimator and the wave energy converters data set is given to test the efficiency of this estimator in denoising.