Multivariate models with constraints: confidence regions. (English) Zbl 1165.62043

Summary: In multivariate linear statistical models with normally distributed observation matrix the structure of the covariance matrix plays an important role when confidence regions must be determined. In this paper it is assumed that the covariance matrix is a linear cornbination of known symmetric and positive semidefinite matrices and unknown parameters (variance components) which are unbiasedly estimable. Then insensitivity regions are found for them which enable us to decide whether a plug-in approach can be used for confidence regions.


62H12 Estimation in multivariate analysis
62J05 Linear regression; mixed models
62F30 Parametric inference under constraints
62F25 Parametric tolerance and confidence regions


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