Statistical Principles and Tangent Models

Abstract

Some recent results in foundational theory are surveyed and some general implications noted. Central to this and focussing on the standard principles of sufficiency and conditionality is an underlying intention of separating error from effect. This manifests itself in the ordinary analysis of variance and also for the generalizations of that analysis for the transformation models and for the exponential models. This paper gives preliminary introduction to the notion of tangent model which in turn allows the partial extension of this error-effect separation to more general statistical models. The emphasis is on finding techniques for determining both significance tests and confidence regions for general models, particularly for complex multiparameter models.