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VOL. 50 | 2006 Corrected confidence intervals for secondary parameters following sequential tests
R. C. Weng, D. S. Coad

Editor(s) Jiayang Sun, Anirban DasGupta, Vince Melfi, Connie Page


Corrected confidence intervals are developed for the mean of the second component of a bivariate normal process when the first component is being monitored sequentially. This is accomplished by constructing a first approximation to a pivotal quantity, and then using very weak expansions to determine the correction terms. The asymptotic sampling distribution of the renormalised pivotal quantity is established in both the case where the covariance matrix is known and when it is unknown. The resulting approximations have a simple form and the results of a simulation study of two well-known sequential tests show that they are very accurate. The practical usefulness of the approach is illustrated by a real example of bivariate data. Detailed proofs of the main results are provided.


Published: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1268.62096
MathSciNet: MR2409065

Digital Object Identifier: 10.1214/074921706000000617

Primary: 62E20 , 62F25 , 62L05 , 65L10

Keywords: approximately pivotal quantity , bivariate normal process , coverage probability , posterior distribution , Stein's identity , very weak expansion

Rights: Copyright © 2006, Institute of Mathematical Statistics


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