Abstract
The paper deals with the problem of finding a better predictor starting from a given one. After introducing some basic notions of sufficiency in terms of a 'sigma-field', a theorem due to K. Tacheuchi and M. Akahira is used to show criterion leading to a better predictor similar to Rao-Blackwell in statistical estimation theory. Then the wide sense sufficiency is introduced showing a criterion to get a better predictor in presence of a sufficient 'sigma-field ' in a wide sense.
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