Within the current paintings i would like to teach a mathematical examine of the statistical thought of sufficiency usually for undominated statistical experiments. The well-known Burkholder's (1961) and Pitcher's(1957) examples stimulated a few researchers to boost new conception of sufficiency. Le Cam (1964) is one of the excellent paper during this box of research. This observe additionally belongs to an analogous zone. although it really is extra restrictive than Le Cam's paper(1964), a research that is attached extra without delay with the classical papers of Halmos and Savage(1949) , and Bahadur(1954) is proven. specifically i need to strengthen a learn according to the concept of pivotal degree which used to be brought via Halmos and Savage(1949) . it really is nice excitement to have this chance to thank Professor H. Heyer and Professor H. Morimoto for his or her cautious analyzing the manuscript and useful reviews on it. i'm additionally grateful to Professor H. Luschgy and Professor D. Mussmann for thei r inspiration of wr i ting "the note". i need to commit this notice to the reminiscence of my father Eizo.
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