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One for All and All for One : Regression Checks with Many Regressors”

  • Pascal Lavergne

    (Crest)

  • Valentin Patilea

    (Crest)

We develop a novel approach to build consistent checks of parametric re-gression models when many regressors are present, based on a class of richenough semiparametric alternatives, namely single-index models. We proposean omnibus test based on the kernel method that performs against a sequenceof directional nonparametric alternatives as if there was one regressor only,whatever the number of regressors. This test can be viewed as a smooth ver-sion of the integrated conditional moment (ICM) test of Bierens. Qualitativeinformation can be easily incorporated in the procedure to enhance power.Our test is little sensitive to the smoothing parameter and performs betterthan several known lack-of-¯t tests in multidimensional settings.

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Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2007-12.

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Length: 28
Date of creation: 2007
Date of revision:
Handle: RePEc:crs:wpaper:2007-12
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  1. Mankiw, N Gregory & Romer, David & Weil, David N, 1992. "A Contribution to the Empirics of Economic Growth," The Quarterly Journal of Economics, MIT Press, vol. 107(2), pages 407-37, May.
  2. Lavergne, Pascal & Patilea, Valentin, 2008. "Breaking the curse of dimensionality in nonparametric testing," Journal of Econometrics, Elsevier, vol. 143(1), pages 103-122, March.
  3. Miguel A. DELGADO & Manuel A. DOMINGUEZ & Pascal LAVERGNE, 2006. "Consistent Tests of Conditional Moment Restrictions," Annales d'Economie et de Statistique, ENSAE, issue 81, pages 33-67.
  4. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-58, November.
  5. Miles, Daniel & Mora, Juan, 2003. "On the performance of nonparametric specification tests in regression models," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 477-490, March.
  6. Fan J. & Huang L-S., 2001. "Goodness-of-Fit Tests for Parametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 640-652, June.
  7. Azzalini,A. & Bowman,A.W. & Haerdle,W., 1988. "On the use of nonparametric regression for model checking," Discussion Paper Serie A 195, University of Bonn, Germany.
  8. Bierens, H.J. & Ploberger, W., 1995. "Asymptotic theory of integrated conditional moment tests," Discussion Paper 1995-124, Tilburg University, Center for Economic Research.
  9. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2003. "Empirical likelihood estimation and consistent tests with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 117(1), pages 55-93, November.
  10. Emmanuel Guerre & Pascal Lavergne, 2004. "Data-Driven Rate-Optimal Specification Testing In Regression Models," Econometrics 0411008, EconWPA.
  11. Juan Carlos Escanciano, 2005. "Goodness-of-fit Tests for Linear and Non-linear Time Series Models," Faculty Working Papers 02/05, School of Economics and Business Administration, University of Navarra.
  12. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
  13. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
  14. Godfrey, Leslie G. & Orme, Chris D., 2004. "Controlling the finite sample significance levels of heteroskedasticity-robust tests of several linear restrictions on regression coefficients," Economics Letters, Elsevier, vol. 82(2), pages 281-287, February.
  15. King, Robert G & Levine, Ross, 1993. "Finance and Growth: Schumpeter Might Be Right," The Quarterly Journal of Economics, MIT Press, vol. 108(3), pages 717-37, August.
  16. Gozalo, Pedro L., 1997. "Nonparametric bootstrap analysis with applications to demographic effects in demand functions," Journal of Econometrics, Elsevier, vol. 81(2), pages 357-393, December.
  17. Juan Carlos Escanciano, 2005. "A Consistent Diagnostic Test for Regression Models Using Projections," Faculty Working Papers 09/05, School of Economics and Business Administration, University of Navarra.
  18. Liu, Zhenjuan & Stengos, Thanasis, 1999. "Non-linearities in Cross-Country Growth Regressions: A Semiparametric Approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 527-38, Sept.-Oct.
  19. Lewbel, Arthur, 1995. "Consistent nonparametric hypothesis tests with an application to Slutsky symmetry," Journal of Econometrics, Elsevier, vol. 67(2), pages 379-401, June.
  20. Li, Q. & Wang, Suojin, 1998. "A simple consistent bootstrap test for a parametric regression function," Journal of Econometrics, Elsevier, vol. 87(1), pages 145-165, August.
  21. Enno Mammen, . "Comparing nonparametric versus parametric regression fits," Statistic und Oekonometrie 9205, Humboldt Universitaet Berlin.
  22. Guerre, Emmanuel & Lavergne, Pascal, 2002. "Optimal Minimax Rates For Nonparametric Specification Testing In Regression Models," Econometric Theory, Cambridge University Press, vol. 18(05), pages 1139-1171, October.
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