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Nonsensitiveness regions in universal models. (English) Zbl 0984.62040
For a linear statistical model without conditions of regularity, unbiased estimators are computed for the expectation \(\mathbf X \beta \) or functions of it. Here, mixed models are considered and it is investigated whether estimates of the covariance structure can destroy the optimum property of the estimator for \(\mathbf X \beta \). A universal model without constraints is defined and expressions for the estimates are developed which enable to determine boundaries of nonsensitiveness regions. Also for models with constraints such regions are found. These are defined in the space of parameters of the covariance matrix of the observation vector; a shift of these parameters inside the nonsensitiveness regions does not cause any essential damage of the estimators.

62H12 Estimation in multivariate analysis
62J05 Linear regression; mixed models
62F10 Point estimation
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