Desirable properties, breakdown and efficiency in the linear regression model

The Neyman--Pearson Lemma introduced the concept of optimality into statistics. The derivation of optimal procedures has since dominated non-Bayesian mathematical statistics. This article criticizes the use of optimality as it operates only within a class of models whose adequacy is not checkable on the basis of the optimal procedure. Furthermore empirically indistinguishable models may have radically different optimal procedures. In Section 2 it is argued that the derivation of optimal procedures should be replaced by the construction of procedures with given properties. Section 3 is concerned with one such property, namely a high breakdown point, in the context of the linear regression model. The ability of high breakdown procedures to deal with outliers and non-linearities is discussed. Section 4 deals with the concept of efficiency. It is argued that 'efficiency at the model' it not suitable as a criterion for choosing an estimator as efficiency depends on the choice of the model. Finally in Section 5 the relationship between breakdown and efficiency in the linear regression model is discussed.