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Testing a Parametric Model Against a Semiparametric Alternative

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  • Horowitz, Joel L.
  • Härdle, Wolfgang

Abstract

This paper describes a method for testing a parametric model of the mean of a random variable Y conditional on a vector of explanatory variables X against a semiparametric alternative. The test is motivated by a conditional moment test against a parametric alternative and amounts to replacing the parametric alternative model with a semiparametric model. The resulting semiparametric test is consistent against a larger set of alternatives than are parametric conditional moments tests based on finitely many moment conditions. The results of Monte Carlo experiments and an application illustrate the usefulness of the new test.

Suggested Citation

  • Horowitz, Joel L. & Härdle, Wolfgang, 1994. "Testing a Parametric Model Against a Semiparametric Alternative," Econometric Theory, Cambridge University Press, vol. 10(05), pages 821-848, December.
  • Handle: RePEc:cup:etheor:v:10:y:1994:i:05:p:821-848_00
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    1. González-Manteiga, Wenceslao & Quintela-del-Río, Alejandro & Vieu, Philippe, 2002. "A note on variable selection in nonparametric regression with dependent data," Statistics & Probability Letters, Elsevier, vol. 57(3), pages 259-268, April.
    2. Grant, Darren, 2016. "The essential economics of threshold-based incentives: Theory, estimation, and evidence from the Western States 100," Journal of Economic Behavior & Organization, Elsevier, vol. 130(C), pages 180-197.
    3. Töpfer, Marina, 2017. "Detailed RIF decomposition with selection: The gender pay gap in Italy," Hohenheim Discussion Papers in Business, Economics and Social Sciences 26-2017, University of Hohenheim, Faculty of Business, Economics and Social Sciences.
    4. Ellison, Glenn & Ellison, Sara Fisher, 2000. "A simple framework for nonparametric specification testing," Journal of Econometrics, Elsevier, vol. 96(1), pages 1-23, May.
    5. 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.
    6. Darren Grant, 2010. "The Simple Economics of Thresholds: Evidence from the Western States 100," Working Papers 1004, Sam Houston State University, Department of Economics and International Business.
    7. 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.
    8. León, Carmelo J. & Araña, Jorge E. & Hanemann, W. Michael & Riera, Pere, 2014. "Heterogeneity and emotions in the valuation of non-use damages caused by oil spills," Ecological Economics, Elsevier, vol. 97(C), pages 129-139.
    9. Chen, Xiaohong & Hong, Han & Shum, Matthew, 2007. "Nonparametric likelihood ratio model selection tests between parametric likelihood and moment condition models," Journal of Econometrics, Elsevier, vol. 141(1), pages 109-140, November.
    10. Herwartz, H. & Xu, F., 2009. "A new approach to bootstrap inference in functional coefficient models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2155-2167, April.
    11. Li, Qi & Hsiao, Cheng & Zinn, Joel, 2003. "Consistent specification tests for semiparametric/nonparametric models based on series estimation methods," Journal of Econometrics, Elsevier, vol. 112(2), pages 295-325, February.
    12. Ait-Sahalia, Yacine & Bickel, Peter J. & Stoker, Thomas M., 2001. "Goodness-of-fit tests for kernel regression with an application to option implied volatilities," Journal of Econometrics, Elsevier, vol. 105(2), pages 363-412, December.
    13. Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, vol. 92(1), pages 101-147, September.
    14. Escanciano, Juan Carlos & Jacho-Chávez, David T., 2010. "Approximating the critical values of Cramér-von Mises tests in general parametric conditional specifications," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 625-636, March.

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