## Institute of Mathematical Statistics Lecture Notes - Monograph Series

- Lecture Notes--Monograph Series
- Number 50, 2006, 80-104

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

R. C. Weng and D. S. Coad

#### Abstract

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.

#### Chapter information

**Source***Recent Developments in Nonparametric Inference and Probability: Festschrift for Michael Woodroofe* (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006)

**Dates**

First available in Project Euclid: 28 November 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.lnms/1196284054

**Digital Object Identifier**

doi:10.1214/074921706000000617

**Mathematical Reviews number (MathSciNet)**

MR2409065

**Zentralblatt MATH identifier**

1268.62096

**Subjects**

Primary: 62E20: Asymptotic distribution theory 62F25: Tolerance and confidence regions 62L05: Sequential design 65L10: Boundary value problems

**Keywords**

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

**Rights**

Copyright © 2006, Institute of Mathematical Statistics

#### Citation

Weng, R. C.; Coad, D. S. Corrected confidence intervals for secondary parameters following sequential tests. Recent Developments in Nonparametric Inference and Probability, 80--104, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000617. https://projecteuclid.org/euclid.lnms/1196284054