Relative squared error prediction in the generalized linear regression model

In linear regression models, predictors based on least squares or on generalized least squares estimators are usually applied which, however, fail in case of multicollinearity. As an alternative biased estimators like ridge estimators, Kuks-Olman estimators, Bayes or minimax estimators are sometimes suggested. In our analysis the relative instead of the generally used absolute squared error enters the objective function. An explicit minimax solution is derived which, in an important special case, can be viewed as a predictor based on a Kuks-Olman estimator.