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Construction of fixed width confidence intervals for a Bernoulli success probability using sequential sampling: a simulation study

Construction of fixed width confidence intervals for a Bernoulli success probability using sequential sampling: a simulation study
Construction of fixed width confidence intervals for a Bernoulli success probability using sequential sampling: a simulation study
This article considers the construction of level 1?? fixed width 2d confidence intervals for a Bernoulli success probability p, assuming no prior knowledge about p and so p can be anywhere in the interval [0, 1]. It is shown that some fixed width 2d confidence intervals that combine sequential sampling of Hall [Asymptotic theory of triple sampling for sequential estimation of a mean, Ann. Stat. 9 (1981), pp. 1229–1238] and fixed-sample-size confidence intervals of Agresti and Coull [Approximate is better than ‘exact’ for interval estimation of binomial proportions, Am. Stat. 52 (1998), pp. 119–126], Wilson [Probable inference, the law of succession, and statistical inference, J. Am. Stat. Assoc. 22 (1927), pp. 209–212] and Brown et al. [Interval estimation for binomial proportion (with discussion), Stat. Sci. 16 (2001), pp. 101–133] have close to 1?? confidence level. These sequential confidence intervals require a much smaller sample size than a fixed-sample-size confidence interval. For the coin jamming example considered, a fixed-sample-size confidence interval requires a sample size of 9457, while a sequential confidence interval requires a sample size that rarely exceeds 2042
0094-9655
1483-1493
Zhou, Sanyu
8b006abb-cfc9-4099-94b3-a6f9a034decf
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Zhou, Sanyu
8b006abb-cfc9-4099-94b3-a6f9a034decf
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a

Zhou, Sanyu and Liu, Wei (2011) Construction of fixed width confidence intervals for a Bernoulli success probability using sequential sampling: a simulation study. Journal of Statistical Computation and Simulation, 81 (11), 1483-1493. (doi:10.1080/00949655.2010.492473).

Record type: Article

Abstract

This article considers the construction of level 1?? fixed width 2d confidence intervals for a Bernoulli success probability p, assuming no prior knowledge about p and so p can be anywhere in the interval [0, 1]. It is shown that some fixed width 2d confidence intervals that combine sequential sampling of Hall [Asymptotic theory of triple sampling for sequential estimation of a mean, Ann. Stat. 9 (1981), pp. 1229–1238] and fixed-sample-size confidence intervals of Agresti and Coull [Approximate is better than ‘exact’ for interval estimation of binomial proportions, Am. Stat. 52 (1998), pp. 119–126], Wilson [Probable inference, the law of succession, and statistical inference, J. Am. Stat. Assoc. 22 (1927), pp. 209–212] and Brown et al. [Interval estimation for binomial proportion (with discussion), Stat. Sci. 16 (2001), pp. 101–133] have close to 1?? confidence level. These sequential confidence intervals require a much smaller sample size than a fixed-sample-size confidence interval. For the coin jamming example considered, a fixed-sample-size confidence interval requires a sample size of 9457, while a sequential confidence interval requires a sample size that rarely exceeds 2042

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e-pub ahead of print date: 24 October 2011
Published date: 2011
Organisations: Statistics

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Local EPrints ID: 337145
URI: http://eprints.soton.ac.uk/id/eprint/337145
ISSN: 0094-9655
PURE UUID: 9c2d8fb1-88c0-4b80-8384-c8cb6e0e5d1e
ORCID for Wei Liu: ORCID iD orcid.org/0000-0002-4719-0345

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Date deposited: 19 Apr 2012 13:46
Last modified: 15 Mar 2024 02:43

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Author: Sanyu Zhou
Author: Wei Liu ORCID iD

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