COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1606

Hybrid and Size-Corrected Subsample Methods

Donald W.K. Andrews and Patrik Guggenberger

March 2007

This paper considers the problem of constructing tests and confidence intervals (CIs) that have correct asymptotic size in a broad class of non-regular models. The models considered are non-regular in the sense that standard test statistics have asymptotic distributions that are discontinuous in some parameters. It is shown in Andrews and Guggenberger (2005a) that standard fixed critical value, subsample, and b < n bootstrap methods often have incorrect size in such models. This paper introduces general methods of constructing tests and CIs that have correct size. First, procedures are introduced that are a hybrid of subsample and fixed critical value methods. The resulting hybrid procedures are easy to compute and have correct size asymptotically in many, but not all, cases of interest. Second, the paper introduces size-correction and "plug-in" size-correction methods for fixed critical value, subsample, and hybrid tests. The paper also introduces finite-sample adjustments to the asymptotic results of Andrews and Guggenberger (2005a) for subsample and hybrid methods and employs these adjustments in size-correction.

The paper discusses several examples in detail. The examples are: (i) tests when a nuisance parameter may be near a boundary, (ii) CIs in an autoregressive model with a root that may be close to unity, and (iii) tests and CIs based on a post-conservative model selection estimator.

Keywords: Asymptotic size, Autoregressive model, b < n bootstrap, Finite-sample size, Hybrid test, Model selection, Over-rejection, Parameter near boundary, Size correction, Subsample confidence interval, Subsample test

JEL Classification Numbers: C12, C15