Statistical Decision Functions.

Abstract: The foundations of a general theory of statistical decision functions, including the classical non-sequential case as well as the sequential case, was discussed by the author in a previous publication [3]. Several assumptions made in [3] appear, however, to be unnecessarily restrictive (see conditions 1-7, pp. 297 in [3]). These assumptions, moreover, are not always fulfilled for statistical problems in their conventional form. In this paper the main results of [3], as well as several new results, are obtained from a considerably weaker set of conditions which are fulfilled for most of the statistical problems treated in the literature. It seemed necessary to abandon most of the methods of proofs used in [3] (particularly those in section 4 of [3]) and to develop the theory from the beginning. To make the present paper self-contained, the basic definitions already given in [3] are briefly restated in section 2.1.