Admissibility of Estimators in the One Parameter Exponential Family and in Multivariate Location Problems

摘要

We are concerned with problems related to admissibility and minimaxity of estimators in the one parameter exponential family, and with classes of estimators which improve upon the best invariant estimator in multivariate location problems (dimensions p > or =3). In connection with admissibility problems we give sufficient conditions for the admissibility of nonlinear estimators (aX + b)/(Cx + d) in estimating an arbitrary function g(theta) with quadratic loss.