Abstract: In this paper, we introduce a new shrinkage soft-wavelet threshold estimator based on Stein's unbiased risk estimate (SURE) for elliptical and spherical distributions under balanced loss functions. we focus on particular thresholding rules to obtain a new threshold, and thus produce new estimators. In addition, we obtain SURE shrinkage based on nonnegative subset of the mean vector. Finally, we present a simulation to test the validity of the proposed estimator.

Key words and phrases: Balance loss function, elliptically distribution, restricted estimator, shrinkage estimator, soft wavelet estimator, spherically distribution.