Corrected confidence intervals for secondary parameters following sequential tests

Details Corrected confidence intervals for secondary parameters following sequential tests Corrected confidence intervals for secondary parameters following sequential tests

2006-11-22

arxiv.org/abs/math/0611682v1

IMS Lecture Notes--Monograph Series 2006, Vol. 50, 80-104

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/074921706000000617 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/

Scientific paper

10.1214/074921706000000617

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.

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