The distribution of estimators after model selection:large and small sample results

Frequently, parameter estimation is preceded by a data-driven model selection procedure. In such a case traditional distribution theory based on the assumption of an a priori given model is no longer valid. In Pötscher (1991) the asymptotic distribution of estimators that are preceded by model selection has been studied. In this paper we study the small sample distribution and, in particular, evaluate the accuracy of the approximation provided by the asymptotic distribution in small samples. We also show, how one of the assumptions in Potscher (1991) can be weakened substantially.