Translator Disclaimer
September, 1973 On Sequential Distinguishability
Rasul A. Khan
Ann. Statist. 1(5): 838-850 (September, 1973). DOI: 10.1214/aos/1176342505

Abstract

Let $X_1, X_2,\cdots$ be a sequence of independent and identically distributed random variables governed by an unknown member of a countable family $\mathscr{P} = \{P_\theta: \theta \in \Omega\}$ of probability measures. The family $\mathscr{P}$ is said to be sequentially distinguishable if for any $\varepsilon (0 < \varepsilon < 1)$ there exist a stopping time $t$ and a terminal decision function $\delta(X_1,\cdots, X_t)$ such that $P_\theta\{t < \infty\} = 1 \forall\theta\in\Omega$ and $\sup_{\theta\in\Omega} P_\theta(\delta(X_1,\cdots, X_t) \neq \theta) \leqq \varepsilon$. Robbins [12] defined a general stopping time (see Section 2) as an approach to this problem. This paper is a study of this stopping time with applications to some exponential distributions.

Citation

Download Citation

Rasul A. Khan. "On Sequential Distinguishability." Ann. Statist. 1 (5) 838 - 850, September, 1973. https://doi.org/10.1214/aos/1176342505

Information

Published: September, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0274.62058
MathSciNet: MR345355
Digital Object Identifier: 10.1214/aos/1176342505

Subjects:
Primary: 62L10
Secondary: 62L99

Rights: Copyright © 1973 Institute of Mathematical Statistics

JOURNAL ARTICLE
13 PAGES


SHARE
Vol.1 • No. 5 • September, 1973
Back to Top