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Testing functional inequalities

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  • Sokbae 'Simon' Lee

    ()
    (Institute for Fiscal Studies and Seoul National University)

  • Kyungchul Song
  • Yoon-Jae Whang

    (Institute for Fiscal Studies and Seoul National University)

Abstract

This paper develops tests for inequality constraints of nonparametric regression functions. The test statistics involve a one-sided version of L p-type functionals of kernel estimators. Drawing on the approach of Poissonization, this paper establishes that the tests are asymptotically distribution free, admitting asymptotic normal approximation. Furthermore, the tests have nontrivial local power against a certain class of local alternatives converging to the null at the rate of n -1/2 . Some results from Monte Carlo simulations are presented.

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File URL: http://cemmap.ifs.org.uk/wps/cwp1211.pdf
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Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP12/11.

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Date of creation: Feb 2011
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Handle: RePEc:ifs:cemmap:12/11

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References

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  1. Sokbae 'Simon' Lee & Yoon-Jae Whang, 2009. "Nonparametric tests of conditional treatment effects," CeMMAP working papers CWP36/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Horowitz, Joel L & Spokoiny, Vladimir G, 2001. "An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model against a Nonparametric Alternative," Econometrica, Econometric Society, vol. 69(3), pages 599-631, May.
  3. Donald W.K. Andrews & Xiaoxia Shi, 2011. "Nonparametric Inference Based on Conditional Moment Inequalities," Cowles Foundation Discussion Papers 1840RR, Cowles Foundation for Research in Economics, Yale University, revised Oct 2013.
  4. Hall, Peter & Yatchew, Adonis, 2005. "Unified approach to testing functional hypotheses in semiparametric contexts," Journal of Econometrics, Elsevier, vol. 127(2), pages 225-252, August.
  5. Liran Einav & Amy Finkelstein & Jonathan Levin, 2010. "Beyond Testing: Empirical Models of Insurance Markets," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 311-336, 09.
  6. Delgado, Miguel A. & Escanciano, Juan Carlos, 2012. "Distribution-free tests of stochastic monotonicity," Journal of Econometrics, Elsevier, vol. 170(1), pages 68-75.
  7. Pierre-André Chiappori & Bruno Jullien & Bernard Salanié & François Salanié, 2002. "Asymmetric Information in Insurance : General Testable Implications," Working Papers 2002-42, Centre de Recherche en Economie et Statistique.
  8. Durot, Cécile, 2003. "A Kolmogorov-type test for monotonicity of regression," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 425-433, July.
  9. Donald W.K. Andrews, 2011. "Similar-on-the-Boundary Tests for Moment Inequalities Exist, But Have Poor Power," Cowles Foundation Discussion Papers 1815R, Cowles Foundation for Research in Economics, Yale University, revised Mar 2012.
  10. Anderson, Gordon & Linton, Oliver & Whang, Yoon-Jae, 2012. "Nonparametric estimation and inference about the overlap of two distributions," Journal of Econometrics, Elsevier, vol. 171(1), pages 1-23.
  11. Gao, Jiti & Gijbels, Irène, 2008. "Bandwidth Selection in Nonparametric Kernel Testing," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1584-1594.
  12. Jushan Bai, 2003. "Testing Parametric Conditional Distributions of Dynamic Models," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 531-549, August.
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Cited by:
  1. Andrews, Donald W.K. & Shi, Xiaoxia, 2014. "Nonparametric inference based on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 179(1), pages 31-45.
  2. Sokbae 'Simon' Lee & Kyungchul Song & Yoon-Jae Whang, 2014. "Testing for a general class of functional inequalities," CeMMAP working papers CWP09/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  3. Donald W. K. Andrews & Xiaoxia Shi, 2013. "Inference Based on Conditional Moment Inequalities," Econometrica, Econometric Society, vol. 81(2), pages 609-666, 03.
  4. Elena Krasnokutskaya & Kyungchul Song & Xun Tang, 2013. "The Role of Quality in Service Markets Organized as Multi-Attribute Auctions," PIER Working Paper Archive 13-053, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  5. Chen, Le-Yu & Szroeter, Jerzy, 2014. "Testing multiple inequality hypotheses: A smoothed indicator approach," Journal of Econometrics, Elsevier, vol. 178(P3), pages 678-693.
  6. Andres Aradillas-Lopez & Adam Rosen, 2013. "Inference in ordered response games with complete information," CeMMAP working papers CWP33/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  7. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2013. "Testing many moment inequalities," CeMMAP working papers CWP65/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  8. Timothy B. Armstrong & Hock Peng Chan, 2013. "Multiscale Adaptive Inference on Conditional Moment Inequalities," Cowles Foundation Discussion Papers 1885, Cowles Foundation for Research in Economics, Yale University.

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