ON TWO NECESSARY-FIELDS AND ON UNIVERSAL LOSSFUNCTIONS
Andrzej Kozek
Abstract: It is shown that the class of best unbiased estimators can be characterized by two
necessary -fields and . The ”large” -field is a makeshift of the minimal
sufficient -field whereas the ”small” -field is a makeshift of the maximal complete
-field. Each estimator which is best unbiased for a strictly convex loss function is
-measurable. Every -measurable estimator is best unbiased for arbitrary convex
loss. Relations of properties of and with the structure of the class of best
unbiased estimators and with properties of universal loss functions are investigated.