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An Adaptive, Rate-Optimal Test of a Parametric Model Against a Nonparametric Alternative

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Author Info

  • Horowitz, Joel L.

    ()
    (University of Iowa)

  • Spokoiny, Vladimir G.

    (Weierstrass Institute for Applied Stochastics)

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    Abstract

    We develop a new test of a parametric model of a conditional mean function against a nonparametric alternative. The test adapts to the unknown smoothness of the alternative model and is uniformly consistent against alternatives whose distance from the parametric model converges to zero at the fastest possible rate. This rate is slower than n-1/2. Some existing tests have non-trivial power against restricted classes of alternatives whose distance from the parametric model decreases at the rate n-1/2. There are, however, sequences of alternatives against which these tests are inconsistent and ours is consistent. As a consequence, there are alternative models for which the finite-sample power of our test greatly exceeds that of existing tests. This conclusion is illustrated by the results of some Monte Carlo experiments.

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    File URL: http://www.biz.uiowa.edu/faculty/horowitz/papers/Atest.pdf
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    Bibliographic Info

    Paper provided by University of Iowa, Department of Economics in its series Working Papers with number 99-02.

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    Length: 38 pages
    Date of creation: Jan 1999
    Date of revision:
    Handle: RePEc:uia:iowaec:99-02

    Contact details of provider:
    Postal: University of Iowa, Department of Economics, Henry B. Tippie College of Business, Iowa City, Iowa 52242
    Phone: (319) 335-0829
    Fax: (319) 335-1956
    Web page: http://tippie.uiowa.edu/economics/
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    Related research

    Keywords: Hypothesis testing; local alternative; uniform consistency; asymptotic power;

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    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. 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.
    2. Yoon-Jae Whang & Donald W.K. Andrews, 1991. "Tests of Specification for Parametric and Semiparametric Models," Cowles Foundation Discussion Papers 968, Cowles Foundation for Research in Economics, Yale University.
    3. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-59, September.
    4. repec:cup:etheor:v:8:y:1992:i:4:p:435-51 is not listed on IDEAS
    5. Whang, Yoon-Jae, 2000. "Consistent bootstrap tests of parametric regression functions," Journal of Econometrics, Elsevier, vol. 98(1), pages 27-46, September.
    6. Härdle, Wolfgang & Sperlich, Stefan & Spokoiny, Vladimir G., 1997. "Component analysis for additive models," SFB 373 Discussion Papers 1997,52, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    7. Yatchew, Adonis John, 1992. "Nonparametric Regression Tests Based on Least Squares," Econometric Theory, Cambridge University Press, vol. 8(04), pages 435-451, December.
    8. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
    9. 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.
    10. repec:wop:humbsf:1997-52 is not listed on IDEAS
    11. repec:cup:etheor:v:8:y:1992:i:4:p:452-75 is not listed on IDEAS
    12. Donald W. K. Andrews, 1997. "A Conditional Kolmogorov Test," Econometrica, Econometric Society, vol. 65(5), pages 1097-1128, September.
    13. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
    14. 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.
    15. Aït-Sahalia, Yacine. & Bickel, Peter J. & Stoker, Thomas M., 1994. "Goodness-of-fit tests for regression using kernel methods," Working papers 3747-94., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    16. Wooldridge, Jeffrey M., 1992. "A Test for Functional Form Against Nonparametric Alternatives," Econometric Theory, Cambridge University Press, vol. 8(04), pages 452-475, December.
    17. 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.
    18. 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.
    19. repec:cup:etheor:v:9:y:1993:i:3:p:451-77 is not listed on IDEAS
    20. de Jong, Robert M., 1996. "The Bierens test under data dependence," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 1-32.
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    Cited by:
    1. Gozalo, Pedro L. & Linton, Oliver B., 2001. "Testing additivity in generalized nonparametric regression models with estimated parameters," Journal of Econometrics, Elsevier, vol. 104(1), pages 1-48, August.
    2. Ignacio N. Lobato, 2000. "A Consistent Test for the Martingale Difference Assumption," Econometric Society World Congress 2000 Contributed Papers 0278, Econometric Society.
    3. Whang, Yoon-Jae, 2000. "Consistent bootstrap tests of parametric regression functions," Journal of Econometrics, Elsevier, vol. 98(1), pages 27-46, September.
    4. Dette, Holger & Hetzler, Benjamin, 2004. "Specification tests indexed by bandwidths," Technical Reports 2004,48, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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