Insensitivity regions for deformation measurement on a dam

Deformation measurement during the filling a dam can be modelled by a multivariate model. Multivariate models usually involve unknown parameters not only in the mean value of the observation matrix but also in the covariance matrix (variance components). The variance components must be estimated and plug-in estimators for the mean value parameters can be used. To find statistical properties of plug-in estimators is rather difficult. In some cases the sensitivity approach can be used. If we know that the true value of the variance components is with sufficiently high probability in so-called insensitivity region, then the plug-in estimator is almost the best linear unbiased estimator. The aim of the paper is to investigate this insensitivity regions, i.e. the region around the true value of variance components, where small changes of them are only of negligible influence on the mean value parameter estimators. The obtained results are applied on the problem of deformation measurement during the filling a dam. Copyright (C) 2009 John Wiley & Sons, Ltd.