Minimax regret comparison of hard and soft thresholding for estimating a bounded normal mean

We study the problem of estimating the mean of a normal distribution with known variance, when prior knowledge specifies that this mean lies in a bounded interval. The focus is on a minimax regret comparison of soft and hard threshold estimators, which have become very popular in the context of wavelet estimation. Under squared-error loss it turns out that soft thresholding is superior to hard thresholding.