PMC Criterion In Prediction Problems Under Loss Function

The PMC(pitman's measure of closeness)criterion has received a great deal of attention in recent years.It seems important to us,however,to obtain the Pitman-closet estimators within the given supposition and a reasonable class of estimators.Under certain conditions,a median unbiased estimator of a parameter is shown to be the Pitman-closest estimator within a certain class of estimators.Then the PMC criterion of estimator problem is applied to predict problems.Under the quadric loss function and linex loss function,median unbiased predictor is proved to be Pitman-closest predictor in assigned predictor set.In this paper,under the normal loss function,median unbiased predictor is proved to be Pitman-closest preditor in assigned predictor set.