Computational Methods for Inference in Nonstandard Testing Problems

Brown University, Providence RI

Investigators

Abstract

This research will develop novel inference procedures for nonstandard hypothesis testing problems that have garnered significant interest among econometricians and statisticians. The first type of nonstandard problems on which it will focus is broadly applicable in fields ranging from industrial organization to finance. Examples include comparisons of competing forecasting models and inference in moment inequality models that seek to reduce heavy assumptions imposed by the researcher. The second type on which it will focus is applicable in nearly all applied fields of the social sciences. For instance, some form of model selection typically is used before a researcher reports the relationships between economic variables estimated from a linear regression model. The pervasiveness of both types of these problems presents substantial challenges to inference in practice. However, their nonstandard nature often is ignored by applied researchers, in part due to the computational complexity required of valid inference. By introducing computationally simplifying techniques founded in new theoretical results, the methods to be developed in this project should further broaden the scope of interest in these nonstandard problems among both econometric theorists and applied researchers, because they will avail sophisticated test construction methods to end-users. This project focuses on two leading classes of nonstandard hypothesis testing problems in econometrics characterized by parameter-discontinuous limit distributions. Though much progress has been made with regard to introducing procedures that uniformly control asymptotic size in these contexts, the computational burden of such procedures can be a major obstacle to their implementation. This research seeks to develop methods to overcome this practical limitation. The first class of these testing problems involves a null hypothesis characterized by a finite number of inequalities. In order to maintain correct asymptotic size and maximize a power criterion, existing approaches to test construction in this context require repeated maximization over an uncountably infinite number of simulated null rejection probabilities. This research will establish theoretical results that substantially reduce the computational burden of test construction by reducing the required search space of null rejection probabilities to a finite set of points. The second class of testing problems involves inference after model selection in the linear regression model. Asymptotically valid tests are to be constructed quite differently under conservative and consistent model selection and the computation of tests under consistent selection can be substantially simpler. The project seeks to exploit the relative computational ease of testing after consistent model selection and establish computationally feasible, powerful, and size-correct testing procedures for inference after model selection.