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Some Higher Order Theory for a Consistent Nonparametric Model Specification Test

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Abstract

We provide second order theory for a smoothing-based model specification test. We derive the asymptotic cumulants and justify an Edgeworth distributional approximation valid to order close to n^{-1}. This is used to define size-corrected critical values whose null rejection frequency improves on the normal critical values. Our simulations confirm the efficacy of this method in moderate sized samples.

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File URL: http://cowles.econ.yale.edu/P/cd/d11a/d1148.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1148.

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Length: 39 pages
Date of creation: Feb 1997
Date of revision:
Publication status: Published in Journal of Statistical Planning and Inference (2003), 109(1-2): 125-154
Handle: RePEc:cwl:cwldpp:1148

Contact details of provider:
Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: Consistent test; Edgeworth expansion; kernel estimation; nonlinear regression;

References

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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  1. repec:cup:etheor:v:12:y:1996:i:1:p:30-60 is not listed on IDEAS
  2. Bierens, H.J. & Ploberger, W., 1995. "Asymptotic theory of integrated conditional moment tests," Discussion Paper 1995-124, Tilburg University, Center for Economic Research.
  3. Bierens, H.J., 1989. "A consistent conditional moment test of functional form," Serie Research Memoranda 0064, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  4. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
  5. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
  6. Fan, Yanqin, 1994. "Testing the Goodness of Fit of a Parametric Density Function by Kernel Method," Econometric Theory, Cambridge University Press, vol. 10(02), pages 316-356, June.
  7. Linton, Oliver, 1996. "Edgeworth Approximation for MINPIN Estimators in Semiparametric Regression Models," Econometric Theory, Cambridge University Press, vol. 12(01), pages 30-60, March.
  8. Donald W.K. Andrews, 1996. "A Conditional Kolmogorov Test," Cowles Foundation Discussion Papers 1111R, Cowles Foundation for Research in Economics, Yale University.
  9. Oliver Linton & Pedro Gozalo, 1996. "Conditional Independence Restrictions: Testing and Estimation," Cowles Foundation Discussion Papers 1140, Cowles Foundation for Research in Economics, Yale University.
  10. repec:cup:etheor:v:10:y:1994:i:2:p:316-56 is not listed on IDEAS
  11. Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-90, July.
  12. repec:cup:etheor:v:9:y:1993:i:3:p:451-77 is not listed on IDEAS
  13. Gozalo, Pedro L., 1993. "A Consistent Model Specification Test for Nonparametric Estimation of Regression Function Models," Econometric Theory, Cambridge University Press, vol. 9(03), pages 451-477, June.
  14. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-59, September.
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Citations

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Cited by:
  1. Fernandes, M. & Grammig, J., 2000. "Non-Parametric Specification Tests for Conditional Duration Models," Economics Working Papers eco2000/4, European University Institute.
  2. Matos, Joao Amaro de & Fernandes, Marcelo, 2004. "Testing the Markov property with ultra-high frequency financial data," FEUNL Working Paper Series wp462, Universidade Nova de Lisboa, Faculdade de Economia.
  3. Marcelo Fernandes & Breno Neri, 2010. "Nonparametric Entropy-Based Tests of Independence Between Stochastic Processes," Econometric Reviews, Taylor & Francis Journals, vol. 29(3), pages 276-306.
  4. Linton, Oliver, 2002. "Edgeworth approximations for semiparametric instrumental variable estimators and test statistics," Journal of Econometrics, Elsevier, vol. 106(2), pages 325-368, February.
  5. Gao, Jiti & Gijbels, Irene, 2005. "Bandwidth selection for nonparametric kernel testing," MPRA Paper 11982, University Library of Munich, Germany, revised Jun 2007.
  6. Gao, Jiti & Casas, Isabel, 2008. "Specification testing in discretized diffusion models: Theory and practice," Journal of Econometrics, Elsevier, vol. 147(1), pages 131-140, November.
  7. Patrick Marsh, . "Nonparametric Likelihood Ratio Tests," Discussion Papers 00/56, Department of Economics, University of York.
  8. Oliver Linton & Pedro Gozalo, 1995. "Testing Additivity in Generalized Nonparametric Regression Models," Cowles Foundation Discussion Papers 1106, Cowles Foundation for Research in Economics, Yale University.

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