Tolerance regions and multiple-use confidence regions in multivariate calibration

Thomas Mathew, Manoj Kumar Sharma, Kenneth Nordström

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

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
Volume26
Issue number5
Publication statusPublished - Oct 1998
Externally publishedYes

Fingerprint

Multivariate Calibration
Confidence Region
Tolerance
Positive definite matrix
Coverage Probability
Statistical Inference
Nonlinear Function
Unknown Parameters
Numerical Computation
Calibration
Multiple use
Confidence region
Unknown
Numerical Results
Requirements

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Mathew, T., Sharma, M. K., & Nordström, K. (1998). Tolerance regions and multiple-use confidence regions in multivariate calibration. Annals of Statistics, 26(5), 1989-2013.

Tolerance regions and multiple-use confidence regions in multivariate calibration. / Mathew, Thomas; Sharma, Manoj Kumar; Nordström, Kenneth.

In: Annals of Statistics, Vol. 26, No. 5, 10.1998, p. 1989-2013.

Research output: Contribution to journalArticle

Mathew, T, Sharma, MK & Nordström, K 1998, 'Tolerance regions and multiple-use confidence regions in multivariate calibration', Annals of Statistics, vol. 26, no. 5, pp. 1989-2013.
Mathew, Thomas ; Sharma, Manoj Kumar ; Nordström, Kenneth. / Tolerance regions and multiple-use confidence regions in multivariate calibration. In: Annals of Statistics. 1998 ; Vol. 26, No. 5. pp. 1989-2013.
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