Specifying Statistical Models

During the last decades. the evolution of theoretical statistics has been marked by a considerable expansion of the number of mathematically and computationaly trac- table models. Faced with this inflation. applied statisticians feel more and more un- comfortable: they are often hesitant about their traditional (typically parametric) assumptions. such as normal and i. i. d . * ARMA forms for time-series. etc . * but are at the same time afraid of venturing into the jungle of less familiar models. The prob- lem of the justification for taking up one model rather than another one is thus a crucial one. and can take different forms. (a) ~~~GBPifi~~~iQ~ : Do observations suggest the use of a different model from the one initially proposed (e. g. one which takes account of outliers). or do they render plau- sible a choice from among different proposed models (e. g. fixing or not the value of a certai n parameter) ? (b) tlQ~~L~~l!rQ1!iIMHQ~ : How is it possible to compute a "e;distance"e; between a given model and a less (or more) sophisticated one. and what is the technical meaning of such a "e;distance"e; ? (c) BQe~~~~~~ : To what extent do the qualities of a procedure. well adapted to a "e;small"e; model. deteriorate when this model is replaced by a more general one? This question can be considered not only. as usual. in a parametric framework (contamina- tion) or in the extension from parametriC to non parametric models but also.