Rukhin, A.
(2009),
Conservative Confidence Ellipsoids for Linear Model Parameters, Mathematical Methods of Statistics, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=902054
(Accessed October 14, 2025)
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Conservative Confidence Ellipsoids for Linear Model Parameters
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Author(s)
Abstract
This paper studies properties of conservative confidence ellipsoids for parameters of a general linear model. These regions are obtained on the basis of a linear estimator when only a vague knowledge of (heterogeneous) error variances is available. The required optimization problem is formulated and the solution space is described. The relationship of this problem to moments of quadratic forms in Gaussian random variables and to multiple hypergeometric functions is demonstrated. We explore the situation when the least favorable variances are equal. An example of a telephone switching study is considered.Citation
Mathematical Methods of Statistics
Volume
18
Issue
4
Pub Type
Journals
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Keywords
Binet-Cauchy formula, Compound matrices, Dirichlet averages, Elementary symmetric functions, Elliptic integrals, Meta-analysis, Multilinear forms, Quadratic forms in normal vectors, Schur product, Zonal polynomials.
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Created December 1, 2009, Updated February 19, 2017