## The Annals of Statistics

### On Asymptotically Optimal Sequential Bayes Interval Estimation Procedures

#### Abstract

A theory of sequential Bayes interval estimation procedures for a single parameter is developed for the case where the loss for using an interval $I$ is a linear combination of the length of $I$, the indicator of noncoverage of $I$, and the number of observations taken. A class of stopping rules $\{t(c): c > 0\}$ is shown to be asymptotically pointwise optimal (A.P.O.) and asymptotically optimal (A.O.) for the confidence interval problem as the cost $c$ per observation tends to 0. The results require generalization of Bickel and Yahav's (1968) general conditions for the existence of A.P.O. and A.O. stopping rules to the case where the terminal risk $Y_n$ satisfies $f(n)Y_n \rightarrow V$ for $f(n)$ a regularly varying function on the integers.

#### Article information

Source
Ann. Statist., Volume 4, Number 4 (1976), 685-711.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176343542

Digital Object Identifier
doi:10.1214/aos/1176343542

Mathematical Reviews number (MathSciNet)
MR426323

Zentralblatt MATH identifier
0339.62059

JSTOR