MODIFIED SHRINKAGE ESTIMATES IN THE EXPONENTIAL FAMILY CASE

According to Shah and Parmar [1], the modified shrunken estimator of the population mean is of the form theta(s) = ptheta + mtheta0, where theta is an unbiased estimator, theta0 is a prior value for theta, p and m are suitable constants. We will show that Bayes estimators with conjugate prior distributions can be used as modified shrunken estimators, and thus the derivation of such estimators can easily be established for the general one parameter exponential family.