Modified large-sample confidence intervals for linear combinations of variance components: Extension, theory, and application

Journal Article (Journal Article)

We consider the problem of setting a confidence interval or bound for a linear combination of variance components related to a multivariate normal distribution, which includes important applications such as comparing variance components and testing the bioequivalence between two drug products. The lack of an exact confidence interval for a general linear combination of variance components spurred the development of a modified large-sample (MLS) method that was shown to be superior to many other approximation methods. But existing MLS method requires the use of independent estimators of variance components. Using a chi-squared representation of a quadratic form of a multivariate normal vector, we extend the MLS method to situations in which estimators of variance components are dependent. Using Edgeworth and Cornish-Fisher expansions, we explicitly derive the second-order asymptotic coverage error of the MLS confidence bound. Our results show that the MLS confidence bound is not second-order accurate in general, but is much better than the confidence bound based on normal approximation and is nearly second-order accurate in some special cases. Our results also show how to construct an MLS confidence bound that is second-order accurate. As an application, we discuss the use of the MLS method in assessing population bioequivalence, with some simulation results and an example.

Full Text

Duke Authors

Cited Authors

  • Lee, Y; Shao, J; Chow, SC

Published Date

  • June 1, 2004

Published In

Volume / Issue

  • 99 / 466

Start / End Page

  • 467 - 478

International Standard Serial Number (ISSN)

  • 0162-1459

Digital Object Identifier (DOI)

  • 10.1198/016214504000000322

Citation Source

  • Scopus