Abstract In linear regression biased estimators like ridge estimators, Kuks–Olman estimators, Bayes, and minimax estimators are mainly used in order to circumvent difficulties caused by multicollinearity. Up to now, the application of the minimax principle to the weighted scalar mean squared error yields explicit solutions solely in specific cases, where, e.g., ridge estimators or Kuks–Olman estimators are obtained. In this paper we introduce a new objective function in such a way that we always get an explicit minimax solution which, in an important special case, can be interpreted as a Kuks–Olman estimator. Our functional may be viewed as a measure of relative rather than absolute squared error.
B. Arnold, P. Stahlecker
Journal of Statistical Planning and Inference