## The Annals of Statistics

### A Note on Bahadur's Transitivity

Eitan Greenshtein

#### Abstract

Let $X_1, X_2, \cdots$ be a sequence of random variables, $(X_1, \cdots, X_n) \sim F^n_\theta, \theta \in \Theta$. In a work by Bahadur it was shown that, for some sequential problems, an inference may be based on a sequence of sufficient and transitive statistics $S_n = S_n(X_1, \cdots, X_n)$ without any loss in statistical performance. A simple criterion for transitivity is given in Theorem 1.

#### Article information

Source
Ann. Statist., Volume 21, Number 4 (1993), 2163-2167.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176349417

Digital Object Identifier
doi:10.1214/aos/1176349417

Mathematical Reviews number (MathSciNet)
MR1245788

Zentralblatt MATH identifier
0799.62088

JSTOR