multivariate model; constraints; variance components; plug-in estimator; insensitivity region
In multivariate linear statistical models with normally distributed observation matrix a structure of a covariance matrix plays an important role when confidence regions must be determined. In the paper it is assumed that the covariance matrix is a linear combination of known symmetric and positive semidefinite matrices and unknown parameters (variance components) which are unbiasedly estimable. Then insensitivity regions are found for them which enables us to decide whether plug-in approach can be used for confidence regions.
 Anderson T. W.: Introduction to Multivariate Statistical Analysis. : J. Wiley, New York
. 1958. MR 0091588
 Fišerová E., Kubáček L., Kunderová P.: Linear Statistical Models: Regularity, Singularities. : Academia, Praha. 2007.
 Kshirsagar A. M.: Multivariate Analysis. : M. Dekker, New York
. 1972. MR 0343478
 Kubáček L., Kubáčková L., Volaufová J.: Statistical Models with Linear Structures. : Veda (Publishing House of Slovak Academy of Sciences), Bratislava. 1995.
 Rao C. R.: Linear Statistical Inference, Its Applications. : J. Wiley, New York–London–Sydney
. 1965. MR 0221616