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Testing functional inequalities

  • Lee, Sokbae
  • Song, Kyungchul
  • Whang, Yoon-Jae

This paper develops tests for inequality constraints of nonparametric regression functions. The test statistics involve a one-sided version of Lp-type functionals of kernel estimators (1≤p<∞). Drawing on the approach of Poissonization, this paper establishes that the tests are asymptotically distribution free, admitting asymptotic normal approximation. In particular, the tests using the standard normal critical values have asymptotically correct size and are consistent against general fixed alternatives. Furthermore, we establish conditions under which the tests have nontrivial local power against Pitman local alternatives. Some results from Monte Carlo simulations are presented.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 172 (2013)
Issue (Month): 1 ()
Pages: 14-32

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Handle: RePEc:eee:econom:v:172:y:2013:i:1:p:14-32
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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. Donald W.K. Andrews & Xiaoxia Shi, 2011. "Nonparametric Inference Based on Conditional Moment Inequalities," Cowles Foundation Discussion Papers 1840R, Cowles Foundation for Research in Economics, Yale University, revised Feb 2013.
  3. Durot, Cécile, 2003. "A Kolmogorov-type test for monotonicity of regression," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 425-433, July.
  4. 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.
  5. Delgado, Miguel A. & Escanciano, Juan Carlos, 2012. "Distribution-free tests of stochastic monotonicity," Journal of Econometrics, Elsevier, vol. 170(1), pages 68-75.
  6. Einav, Liran & Finkelstein, Amy & Levin, Jonathan, 2009. "Beyond Testing: Empirical Models of Insurance Markets," Department of Economics, Working Paper Series qt90g407hf, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  7. 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.
  8. 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.
  9. Sokbae Lee & Yoon-Jae Whang, 2009. "Nonparametric Tests of Conditional Treatment Effects," Cowles Foundation Discussion Papers 1740, Cowles Foundation for Research in Economics, Yale University.
  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. 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.
  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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