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Toutenburg, Helge; Fieger, A.; Schaffrin, B. (1999): Approximate Confidence Regions for Minimax-Linear Estimators. Collaborative Research Center 386, Discussion Paper 166


Minimax estimation is based on the idea, that the quadratic risk function for the estimate β is not minimized over the entire parameter space R^K, but only over an area B(β) that is restricted by a priori knowledge. If all restrictions define a convex area, this area can often be enclosed in an ellipsoid of the form B(β) = { β : β' Tβ ≤ r }. The ellipsoid has a larger volume than the cuboid. Hence, the transition to an ellipsoid as a priori information represents a weakening, but comes with an easier mathematical handling. Deriving the linear Minimax estimator we see that it is biased and non-operationable. Using an approximation of the non-central χ^2-distribution and prior information on the variance, we get an operationable solution which is compared with OLSE with respect to the size of the corresponding confidence intervals.