MULTIPLE SHRINKAGE GENERALIZATIONS OF THE JAMES-STEIN ESTIMATOR

Publisher Summary This chapter discusses the multiple shrinkage generalizations of the James-Stein estimator. James and Stein proposed the first prototype minimax shrinkage estimator. This estimator not only dominates the classical maximum likelihood estimator δMLE = Y in risk, but can also yield very small risk when θ is very close to 0. Because the potential risk reduction offered by over δMLE is large enough to be of practical value, this estimator stimulated the development of a large number of minimax shrinkage estimators which can offer meaningful risk reduction in a region of the parameter space close to a prespecified target. A major practical limitation of currently employed minimax shrinkage estimators is that they offer meaningful risk reduction only in a relatively small region of the parameter space, and are very sensitive to misspecification.