Tolerance regions and multiple-use confidence regions in multivariate calibration

Thomas Mathew, Manoj Kumar Sharma, Kenneth Nordström

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


Let y, ∼ N(Bxi, ∑), i = 1, 2,..., N, and y ∼ N(Bθ, ∑) be independent multivariate observations, where the xi's are known vectors, B, θ and ∑ are unknown, ∑ being a positive definite matrix. The calibration problem deals with statistical inference concerning θ and the problem that we have addressed is the construction of confidence regions. In this article, we have constructed a region for θ based on a criterion similar to that satisfied by a tolerance region. The situation where θ is possibly a nonlinear function, say h(ξ), of fewer unknown parameters denoted by the vector ξ, is also considered. The problem addressed in this context is the construction of a region for ξ. The numerical computations required for the practical implementation of our region are explained in detail and illustrated using an example. Limited numerical results indicate that our regions satisfy the coverage probability requirements of multiple-use confidence regions.

Original languageEnglish
Pages (from-to)1989-2013
Number of pages25
JournalAnnals of Statistics
Issue number5
Publication statusPublished - Oct 1998


  • Calibration
  • Matrix variate F distribution
  • Matrix variate beta distribution
  • Multiple-use confidence region
  • Multivariate linear model
  • Noncentral chi-square
  • Tolerance region
  • Wishart distribution

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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