The Annals of Statistics

Sequential confidence regions for maximum likelihood estimates

A. Dmitrienko and Z. Govindarajulu

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 28, Number 5 (2000), 1472-1501.

Dates
First available in Project Euclid: 12 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1015957403

Digital Object Identifier
doi:10.1214/aos/1015957403

Mathematical Reviews number (MathSciNet)
MR1805793

Zentralblatt MATH identifier
1105.62369

Subjects
Primary: 62L12: Sequential estimation
Secondary: 62F10: Point estimation

Keywords
Sequential methods asymptotic consistency asymptotic efficiency

Citation

Dmitrienko, A.; Govindarajulu, Z. Sequential confidence regions for maximum likelihood estimates. Ann. Statist. 28 (2000), no. 5, 1472--1501. doi:10.1214/aos/1015957403. https://projecteuclid.org/euclid.aos/1015957403


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