Sequential fixed width confidence intervals

Author: Asparouhov, Tihomir Zlatev

Year: 2000

Degree: Dissertation (Ph.D.)

Advisor: Lorden, Gary A.

Committee Member: Unknown, Unknown

Option: Mathematics

DOI: 10.7907/0DZR-RK42

Abstract

We consider the problem of constructing confidence intervals of fixed width d and confidence level γ for the success probability p in Bernoulli trials. Algorithms are given for calculating numerical lower bounds on the average expected sample size required and an asymptotic lower bound is obtained as d -> 0. Sequential and two-stage procedures are proposed that attain the asymptotic lower bounds and nearly attain the numerical lower bounds. Asymptotically optimal sequential and two-stage confidence intervals of fixed width and confidence level are proposed for the mean in a general (non-Bernoulli) context.

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