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Bonferroni-Based Size-Correction for Nonstandard Testing Problems

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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.

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  • Adam McCloskey, 2012. "Bonferroni-Based Size-Correction for Nonstandard Testing Problems," Working Papers 2012-16, Brown University, Department of Economics.
  • Handle: RePEc:bro:econwp:2012-16
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    1. repec:gam:jecnmx:v:5:y:2017:i:2:p:25-:d:101429 is not listed on IDEAS
    2. Xu Cheng, 2014. "Uniform Inference in Nonlinear Models with Mixed Identification Strength," PIER Working Paper Archive 14-018, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    3. repec:gam:jecnmx:v:6:y:2017:i:1:p:1-:d:124889 is not listed on IDEAS
    4. DiTraglia, Francis J., 2016. "Using invalid instruments on purpose: Focused moment selection and averaging for GMM," Journal of Econometrics, Elsevier, vol. 195(2), pages 187-208.
    5. Cheng, Xu & Liao, Zhipeng, 2015. "Select the valid and relevant moments: An information-based LASSO for GMM with many moments," Journal of Econometrics, Elsevier, vol. 186(2), pages 443-464.
    6. Francis J. DiTraglia, 2011. "Using Invalid Instruments on Purpose: Focused Moment Selection and Averaging for GMM, Second Version," PIER Working Paper Archive 14-045, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 09 Dec 2014.
    7. Cheng, Xu, 2015. "Robust inference in nonlinear models with mixed identification strength," Journal of Econometrics, Elsevier, vol. 189(1), pages 207-228.
    8. Timothy B. Armstrong & Michal Kolesár, 2016. "Optimal Inference in a Class of Regression Models," Cowles Foundation Discussion Papers 2043, Cowles Foundation for Research in Economics, Yale University.
    9. Jui-Chung Yang & Ke-Li Xu, 2013. "Estimation and Inference under Weak Identi cation and Persistence: An Application on Forecast-Based Monetary Policy Reaction Function," 2013 Papers pya307, Job Market Papers.
    10. Massimo Franchi & Søren Johansen, 2017. "Improved Inference on Cointegrating Vectors in the Presence of a near Unit Root Using Adjusted Quantiles," Econometrics, MDPI, Open Access Journal, vol. 5(2), pages 1-20, June.
    11. Ivan A. Canay & Azeem M. Shaikh, 2016. "Practical and theoretical advances in inference for partially identified models," CeMMAP working papers CWP05/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    12. Xu Cheng & Zhipeng Liao, 2012. "Select the Valid and Relevant Moments: A One-Step Procedure for GMM with Many Moments," PIER Working Paper Archive 12-045, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

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    Keywords

    Hypothesis testing; uniform inference; asymptotic size; exact size; power; size-correction; model selection; boundary problems; local asymptotics;

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