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Testing functional inequalities

  • Sokbae Lee

    ()

    (Institute for Fiscal Studies and cemmap and SNU)

  • Kyungchul Song

    (Institute for Fiscal Studies)

  • Yoon-Jae Whang

    ()

    (Institute for Fiscal Studies and SNU)

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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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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  1. 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.
  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. 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.
  4. 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.
  5. 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.
  6. Donald W.K. Andrews & Xiaoxia Shi, 2011. "Nonparametric Inference Based on Conditional Moment Inequalities," Cowles Foundation Discussion Papers 1840, Cowles Foundation for Research in Economics, Yale University.
  7. V. Konakov & H. Läuter & H. Liero, 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.
  8. 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.
  9. 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.
  10. 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.
  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. Durot, Cécile, 2003. "A Kolmogorov-type test for monotonicity of regression," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 425-433, July.
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