Partial optimum estimator in two stage regression model with constraints and a problem of equivalence. (English) Zbl 1107.62051

The article considers a two-stage regression model with constraints, a model arising in geodesic network measurements. In the first stage the parameter \(\Theta \) is estimated, and in the second stage the parameter \((\Theta ', \beta ')'\) is to be estimated. The search for an optimal linear estimator can be further complicated by two types of constraints and by the fact that the first stage estimator sometimes must be changed. Since joint efficient linear unbiased estimators do not exist, H-optimal estimators are derived. The question of algorithm equivalence is also briefly discussed. An illustrative numerical example is included.


62J05 Linear regression; mixed models
86A32 Geostatistics
65C60 Computational problems in statistics (MSC2010)


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