Bonferroni-Based Size-Correction for Nonstandard Testing Problems
67 Pages Posted: 6 Nov 2012 Last revised: 8 Jul 2016
Date Written: January 1, 2016
Abstract
We develop a set of powerful and flexible size-correction procedures for general nonstandard testing environments in which the asymptotic distribution of a test statistic is discontinuous in a nuisance parameter under the null hypothesis. Examples of this form of testing problem are pervasive in econometrics and complicate inference by making size difficult to control. The test constructions introduced here simultaneously control the asymptotic size of the test uniformly over the nuisance parameter space while leading to tests with desirable power properties. They have the flexibility to allow the user to direct the power of the resultant test toward alternatives of particular interest. We introduce three types of size-corrected critical values that make use of reasoning derived from Bonferroni bounds. The new methods provide complementary alternatives to existing size-correction methods, entailing substantially higher power for many testing problems. The critical value constructions are developed for an expanded class of testing problems, allowing application in problems to which previously available size-corrections did not apply. We detail the construction and performance of the new tests in examples of testing after conservative and consistent model selection in the linear regression model.
Keywords: Hypothesis testing, uniform inference, asymptotic size, Bonferroni bounds, power, size-correction, model selection, pretesting, local asymptotics
JEL Classification: C12, C51, C52
Suggested Citation: Suggested Citation
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