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Testing functional inequalities

Author

Listed:
  • Sokbae Lee

    () (Institute for Fiscal Studies and Columbia University and IFS)

  • Kyungchui (Kevin) Song

    (Institute for Fiscal Studies)

  • Yoon-Jae Whang

    () (Institute for Fiscal Studies and SNU)

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.

Suggested Citation

  • Sokbae Lee & Kyungchui (Kevin) Song & Yoon-Jae Whang, 2011. "Testing functional inequalities," CeMMAP working papers CWP12/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:12/11
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    File URL: http://cemmap.ifs.org.uk/wps/cwp1211.pdf
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    References listed on IDEAS

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    1. Pierre‐André Chiappori & Bruno Jullien & Bernard Salanié & François Salanié, 2006. "Asymmetric information in insurance: general testable implications," RAND Journal of Economics, RAND Corporation, vol. 37(4), pages 783-798, December.
    2. 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, September.
    3. 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.
    4. Sokbae 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.
    5. 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.
    6. Andrews, Donald W.K. & Shi, Xiaoxia, 2014. "Nonparametric inference based on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 179(1), pages 31-45.
    7. Durot, Cécile, 2003. "A Kolmogorov-type test for monotonicity of regression," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 425-433, July.
    8. 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.
    9. Delgado, Miguel A. & Escanciano, Juan Carlos, 2012. "Distribution-free tests of stochastic monotonicity," Journal of Econometrics, Elsevier, vol. 170(1), pages 68-75.
    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. Donald W.K. Andrews, 2011. "Similar-on-the-Boundary Tests for Moment Inequalities Exist, But Have Poor Power," Cowles Foundation Discussion Papers 1815, Cowles Foundation for Research in Economics, Yale University.
    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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    Citations

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    Cited by:

    1. 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.
    2. repec:eee:econom:v:203:y:2018:i:2:p:241-255 is not listed on IDEAS
    3. Sokbae Lee & Kyungchul Song & Yoon-Jae Whang, 2014. "Testing For A General Class Of Functional Inequalities," KIER Working Papers 889, Kyoto University, Institute of Economic Research.
    4. Donald W. K. Andrews & Xiaoxia Shi, 2013. "Inference Based on Conditional Moment Inequalities," Econometrica, Econometric Society, vol. 81(2), pages 609-666, March.
    5. Horowitz, Joel L. & Lee, Sokbae, 2017. "Nonparametric estimation and inference under shape restrictions," Journal of Econometrics, Elsevier, vol. 201(1), pages 108-126.
    6. Andrews, Donald W.K. & Shi, Xiaoxia, 2014. "Nonparametric inference based on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 179(1), pages 31-45.
    7. 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.
    8. Chen, Le-Yu & Szroeter, Jerzy, 2014. "Testing multiple inequality hypotheses: A smoothed indicator approach," Journal of Econometrics, Elsevier, vol. 178(P3), pages 678-693.
    9. Sainan Jin & Valentina Corradi & Norman Swanson, 2015. "Robust Forecast Comparison," Departmental Working Papers 201502, Rutgers University, Department of Economics.
    10. Armstrong, Timothy B., 2015. "Asymptotically exact inference in conditional moment inequality models," Journal of Econometrics, Elsevier, vol. 186(1), pages 51-65.
    11. 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.
    12. Aradillas-López, Andrés & Gandhi, Amit & Quint, Daniel, 2016. "A simple test for moment inequality models with an application to English auctions," Journal of Econometrics, Elsevier, vol. 194(1), pages 96-115.
    13. Andrews, Donald W.K. & Shi, Xiaoxia, 2017. "Inference based on many conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 196(2), pages 275-287.
    14. Kyungchul Song, 2011. "Testing Predictive Ability and Power Robustification," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(2), pages 288-296, October.
    15. Armstrong, Timothy B. & Chan, Hock Peng, 2016. "Multiscale adaptive inference on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 194(1), pages 24-43.
    16. 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.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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