The problem of approslmatting an unknow 'regression function by an eiement of a given set of functions on the basis of a set of observations is solied in some cases of redu-cibility. The resnlting estimators have optimality properties under wider model assumptions than usual in regression analysis. For instance robustness of least squares estimators agaiiist model errors csn be shown. The related problems arising in experimental design and model choice are discussed.