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Parametric and Non‐parametric Encompassing Procedures

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  • Christophe Bontemps
  • Jean‐Pierre Florens
  • Jean‐François Richard

Abstract

We study the asymptotic behaviour of encompassing statistics in general regression models. The theory for testing one parametric model against another parametric model is now well known, but the comparison of two non‐parametric models, or ‘crossed’ situations where a parametric model is tested against a non‐parametric one, has not been treated previously. The encompassing test statistics for the four cases presented here are based on an appropriately normalized difference between an estimator of parameters (eventually functional), and its pseudo‐true value under . The specification tests for non‐parametrically estimated models have meaning only when the smoothing parameter is not arbitrarily chosen, and so the window widths are calculated by an automatic empirical method (cross‐validation). As the window width determination is part of the estimation procedure, the pseudo‐true window width, associated with the pseudo‐true value, is defined.

Suggested Citation

  • Christophe Bontemps & Jean‐Pierre Florens & Jean‐François Richard, 2008. "Parametric and Non‐parametric Encompassing Procedures," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 751-780, December.
    • Handle: RePEc:bla:obuest:v:70:y:2008:i:s1:p:751-780
    DOI: 10.1111/j.1468-0084.2008.00529.x
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    References listed on IDEAS

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    1. Christophe Bontemps & Grayham E. Mizon, 2008. "Encompassing: Concepts and Implementation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 721-750, December.
    2. Florens, Jean-Pierre & Hendry, David F. & Richard, Jean-François, 1996. "Encompassing and Specificity," Econometric Theory, Cambridge University Press, vol. 12(4), pages 620-656, October.
    3. Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
    4. Mizon, Grayham E & Richard, Jean-Francois, 1986. "The Encompassing Principle and Its Application to Testing Non-nested Hypotheses," Econometrica, Econometric Society, vol. 54(3), pages 657-678, May.
    5. White, Halbert, 1980. "Using Least Squares to Approximate Unknown Regression Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 149-170, February.
    6. Lavergne, Pascal & Patilea, Valentin, 2008. "Breaking the curse of dimensionality in nonparametric testing," Journal of Econometrics, Elsevier, vol. 143(1), pages 103-122, March.
    7. Bontemps, C. & Florens, J.P., 1995. "A Global Encompassing Criterion for Nonparametric Encompassing," Papers 95.386, Toulouse - GREMAQ.
    8. Marron, J S, 1988. "Automatic Smoothing Parameter Selection: A Survey," Empirical Economics, Springer, vol. 13(3/4), pages 187-208.
    9. Govaerts, Bernadette & Hendry, David F. & Richard, Jean-Francois, 1994. "Encompassing in stationary linear dynamic models," Journal of Econometrics, Elsevier, vol. 63(1), pages 245-270, July.
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    1. Christophe Bontemps & Grayham E. Mizon, 2008. "Encompassing: Concepts and Implementation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 721-750, December.

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