ABSTRACT
The idea of sufficiency is an important notion in statistical theory generally as well as in minimum-variance unbiased estimation in particular, so that while the authors discuss it in the latter context it must be borne in mind that it has more general impact. As always, one wishes such approximations to be 'as good as possible', and in order to clarify what they mean by the phrase in an inference context they shall formulate the problem mathematically, considering first on the case where they are interested in a single numerical characteristic. While it is desirable from a theoretical point of view to demonstrate that an estimator is, in some sense, it may be sufficient from a practical point of view to show that some estimator which is being used is nearly the best possible.
