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July, 1976 On Asymptotically Optimal Sequential Bayes Interval Estimation Procedures
Leon Jay Gleser, Sudhakar Kunte
Ann. Statist. 4(4): 685-711 (July, 1976). DOI: 10.1214/aos/1176343542


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.


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Leon Jay Gleser. Sudhakar Kunte. "On Asymptotically Optimal Sequential Bayes Interval Estimation Procedures." Ann. Statist. 4 (4) 685 - 711, July, 1976.


Published: July, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0339.62059
MathSciNet: MR426323
Digital Object Identifier: 10.1214/aos/1176343542

Primary: 62L12
Secondary: 60F99 , 60G40 , 62F10 , 62F15 , 62F25 , 62L15

Keywords: Asymptotically optimal , asymptotically pointwise optimal , Bayes interval estimation procedures , moderate deviation theory , regularly varying function , sequential inference , Stopping rules

Rights: Copyright © 1976 Institute of Mathematical Statistics


Vol.4 • No. 4 • July, 1976
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