Open Access
October2000 Sequential confidence regions for maximum likelihood estimates
A. Dmitrienko, Z. Govindarajulu
Ann. Statist. 28(5): 1472-1501 (October2000). DOI: 10.1214/aos/1015957403


The goal of this paper is to develop a general framework for constructing sequential fixed size confidence regions based on maximum likelihood estimates. Asymptotic properties of the sequential procedure for setting up the confidence regions are analyzed under very broad assumptions on the underlying parametric model. It is shown that the proposed sequential procedure is asymptotically optimal in the sense that it approximates the optimal fixed-sample size procedure. It is further shown that the “cost of ignorance” associated with the sequential procedure is bounded. Applications are made to estimation problems arising in prospective and retrospective studies.


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A. Dmitrienko. Z. Govindarajulu. "Sequential confidence regions for maximum likelihood estimates." Ann. Statist. 28 (5) 1472 - 1501, October2000.


Published: October2000
First available in Project Euclid: 12 March 2002

zbMATH: 1105.62369
MathSciNet: MR1805793
Digital Object Identifier: 10.1214/aos/1015957403

Primary: 62L12
Secondary: 62F10

Keywords: Asymptotic consistency , Asymptotic efficiency , sequential methods

Rights: Copyright © 2000 Institute of Mathematical Statistics

Vol.28 • No. 5 • October2000
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