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Testing functional inequalities

Author

Listed:
  • Sokbae (Simon) Lee

    (Institute for Fiscal Studies and Columbia University)

  • 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 (Simon) 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
    as

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    File URL: http://cemmap.ifs.org.uk/wps/cwp1211.pdf
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    References listed on IDEAS

    as
    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. Donald W. K. Andrews & Xiaoxia Shi, 2013. "Inference Based on Conditional Moment Inequalities," Econometrica, Econometric Society, vol. 81(2), pages 609-666, March.
    4. 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.
    5. 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.
    6. 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.
    7. Andrews, Donald W.K. & Shi, Xiaoxia, 2014. "Nonparametric inference based on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 179(1), pages 31-45.
    8. Durot, Cécile, 2003. "A Kolmogorov-type test for monotonicity of regression," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 425-433, July.
    9. Fan, Yanqin & Li, Qi, 2000. "Consistent Model Specification Tests," Econometric Theory, Cambridge University Press, vol. 16(6), pages 1016-1041, December.
    10. 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.
    11. Delgado, Miguel A. & Escanciano, Juan Carlos, 2012. "Distribution-free tests of stochastic monotonicity," Journal of Econometrics, Elsevier, vol. 170(1), pages 68-75.
    12. 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.
    13. 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.
    14. Pierre‐André Chiappori & Bruno Jullien & Bernard Salanié & François Salanié, 2006. "Asymmetric information in insurance: general testable implications," RAND Journal of Economics, The RAND Corporation, vol. 37(4), pages 783-798, December.
    15. 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.
    16. Konakov, V. & Läuter, H. & Liero, H., 1995. "Nonparametric versus Parametric Goodness of Fit," SFB 373 Discussion Papers 1995,49, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    Full references (including those not matched with items on IDEAS)

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    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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