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

被引:2
|
作者
Liu, Wei [1 ,2 ]
Zhou, Sanyu [3 ]
机构
[1] Univ Southampton, S3RI, Southampton SO17 1BJ, Hants, England
[2] Univ Southampton, Sch Math, Southampton SO17 1BJ, Hants, England
[3] Shanghai Univ Finance & Econ, Sch Stat & Management, Shanghai 200433, Peoples R China
关键词
Bernoulli trials; confidence interval; confidence level; coverage probability; sample size; sequential sampling; statistical simulation; BINOMIAL PROPORTION; ASYMPTOTIC THEORY; APPROXIMATE; PARAMETER; LIMITS;
D O I
10.1080/00949655.2010.492473
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
This article considers the construction of level 1 - alpha 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 - alpha 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.
引用
收藏
页码:1483 / 1493
页数:11
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