Is dominating Positive Part James Stein estimator when estimating the mean of a multivariate normal of dimension 3 with known variance(all equal) an open problem?
If not, what is this estimator called? Can you point out some references?
Yes, there is a published reply to this challenge, by Peter Yi-Shi Shao and William E. Strawderman in 1994: https://projecteuclid.org/euclid.aos/1176325640
They provide conditions on estimators of the type
to ensure domination. Interestingly such estimators are also inadmissible and hence are dominated by other (generalised Bayes) estimators (see p. 1530).