A general Approach to the Construction of Model Diagnostics based upon the Lagrange Multiplier Principle

In order to assess the validity of the specification of an econometric model, it is useful to have a variety of diagnostic statistics which might provide the evidence on the existence and possibly the type of misspecification involved. One source of diagnostics is hypothesis tests where the model under consideration is taken to be the null and the alternative is some general action. A particularly attractive approach is to construct optimal test statistics against a variety of specific alternatives. In this way it is possible to have reasonable power against a collection of interesting alternatives, although when looking at sets of non-independent statistics, one must be cautious about interpretations of the overall size of the test.