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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 1, Fasc. 1,
pages 29 - 47
 

ON TWO NECESSARY s -FIELDS AND ON UNIVERSAL LOSS FUNCTIONS

Andrzej Kozek

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

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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