Tests and Confidence Regions

Abstract

Although testing theory can be perceived as a special case of Decision Theory for a restricted decision space (and even as an estimation problem), we consider testing inference in a separate chapter because there is much more ambiguity about the real inferential purpose of testing than when estimating a regular function of the parameter. In fact, this part of statistical inference is still incomplete, in the sense that many alternative answers have been proposed, none being entirely satisfactory.In particular, there exist strong differences between frequentist and Bayesian testing theories. This is nonetheless a setting where a Bayesian approach is quite appealing, if only because the notion of probability of a hypothesis is well defined. But there are controversies running about noninformative perspectives for point null hypotheses and model choice settings.