Eine Bemerkung zur Existenz erwartungstreuer Schätzer

Summary A theorem ofBickel andLehmann concerning the existence of unbiased estimates for parameters on the convex family of all absolutely continuous probability distributions is generalized to arbitrary convex families of absolutely continuous distributions. In contrast to the result ofBickel andLehmann, however, we give necessary and sufficient conditions for the existence of only approximately unbiased estimates. An example, which is borrowed from density estimation, shows that in general the term approximately cannot be ommitted.