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Testing multiple inequality hypotheses: A smoothed indicator approach

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  • Chen, Le-Yu
  • Szroeter, Jerzy
Abstract
This paper proposes a class of origin-smooth approximators of indicators underlying the sum-of-negative-part statistic for testing multiple inequalities. The need for simulation or bootstrap to obtain test critical values is thereby obviated. A simple procedure is enabled using fixed critical values. The test is shown to have correct asymptotic size in the uniform sense that supremum finite-sample rejection probability over null-restricted data distributions tends asymptotically to nominal significance level. This applies under weak assumptions allowing for estimator covariance singularity. The test is unbiased for a wide class of local alternatives. A new theorem establishes directions in which the test is locally most powerful. The proposed procedure is compared with predominant existing tests in structure, theory and simulation.

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  • Chen, Le-Yu & Szroeter, Jerzy, 2014. "Testing multiple inequality hypotheses: A smoothed indicator approach," Journal of Econometrics, Elsevier, vol. 178(P3), pages 678-693.
    • Handle: RePEc:eee:econom:v:178:y:2014:i:p3:p:678-693
    DOI: 10.1016/j.jeconom.2013.10.004
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    8. Huber, Martin & Wüthrich, Kaspar, 2017. "Evaluating local average and quantile treatment effects under endogeneity based on instruments: a review," FSES Working Papers 479, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
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    More about this item

    Keywords

    Test; Multiple inequalities; One-sided hypothesis; Composite null; Binding constraints; Asymptotic exactness; Covariance singularity; Indicator smoothing;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics

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