統計数理研究所

Abstract: A confidence interval depends on the model as well as the data. We distinguish two types of model: a model which is based on knowledge or assumptions about the background to the data (a scientific model), and a model which is chosen because it gives a good description of the data ( an empirical model). In practice we often choose, or confirm, a model by showing that it gives a good fit to the data using a goodness-of-fit test or graphical diagnostics. However, confidence intervals are calculated on the assumption that the model is fixed and known. This is OK for scientific models, but are confidence intervals valid for empirical models? I will discuss this question by looking at the class of confidence intervals generated by the class of models which would be accepted as good empirical models as judged by a given goodness-of-fit test. Two examples, contingency tables and subset selection in linear regression, suggest some quite general asymptotic theory.