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A note on Bahadur’s transitivity. (English) Zbl 0799.62088
Summary: Let $$X_ 1$$, $$X_ 2,\dots$$ be a sequence of random variables, $$(X_ 1, \dots, X_ n) \sim F_ \theta^ n$$, $$\theta \in \Theta$$. In a work by R. R. Bahadur [Ann. Math. Stat. 25, 432-462 (1954; Zbl 0057.356)] it was shown that, for some sequential problems, an inference may be based on a sequence of sufficient and transitive statistics $$S_ n = S_ n (X_ 1, \dots, X_ n)$$ without any loss in statistical performance. A simple criterion for transitivity is given.

##### MSC:
 62L10 Sequential statistical analysis 62B05 Sufficient statistics and fields 62B99 Sufficiency and information
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