Bonferroni-Based Size-Correction for Nonstandard Testing Problems

Adam McCloskey

No 2012-16, Working Papers from Brown University, Department of Economics

Abstract: We develop powerful new size-correction procedures for nonstandard hypothesis testing environments in which the asymptotic distribution of a test statistic is discontinuous in a parameter under the null hypothesis. Examples of this form of testing problem are pervasive in econometrics and complicate inference by making size di- cult to control. This paper introduces two sets of new size-correction methods that correspond to two di erent general hypothesis testing frameworks. The new methods are designed to maximize the power of the underlying test while maintaining correct asymptotic size uniformly over the parameter space speci ed by the null hypothesis. They involve the construction of critical values that make use of reasoning derived from Bonferroni bounds. The rst set of new methods provides complementary alternatives to existing size-correction methods, entailing substantially higher power for many testing problems. The second set of new methods provides the rst available asymptotically size-correct tests for the general class of testing problems to which it applies. This class includes hypothesis tests on parameters after consistent model selection and tests on super-ecient/hard-thresholding estimators. We detail the construction and performance of the new tests in three speci c examples: testing after conservative model selection, testing when a nuisance parameter may be on a boundary and testing after consistent model selection.

Keywords: Hypothesis testing; uniform inference; asymptotic size; exact size; power; size-correction; model selection; boundary problems; local asymptotics (search for similar items in EconPapers)
Date: 2012
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (20)

Downloads: (external link)
https://economics.brown.edu/sites/g/files/dprerj72 ... rs/2012-16_paper.pdf (application/pdf)

Related works:
Journal Article: Bonferroni-based size-correction for nonstandard testing problems (2017)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bro:econwp:2012-16

Access Statistics for this paper

More papers in Working Papers from Brown University, Department of Economics Department of Economics, Brown University, Providence, RI 02912.
Bibliographic data for series maintained by Brown Economics Webmaster ().