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Testing for Neglected Nonlinearity Using Extreme Learning Machines (published in: International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 21, Suppl. 2 (2013), 117--129.)

Author

Listed:
  • KYU LEE SHIN

    (Educational Research Institute, Inha University)

  • JIN SEO CHO

    (School of Economics, Yonsei University)

Abstract

In this study, we introduce statistics for testing neglected nonlinearity using the extreme leaning machines introduced by Huang, Zhu, and Siew (2006, Neurocomputing) and call them ELMNN tests. The ELMNN tests are very convenient and can be widely applied because they are obtained as byproducts of estimating linear models, and they can serve as quick diagnostic test statistics complementing the computational burdens of other tests. For the proposed test statistics, we provide a set of regularity conditions under which they asymptotically follow a chi-squared distribution under the null and are consistent under the alternative. We conduct Monte Carlo experiments and examine how they behave when the sample size is finite. Our experiment shows that the tests exhibit the properties desired by the theory of this paper.

Suggested Citation

  • Kyu Lee Shin & Jin Seo Cho, 2013. "Testing for Neglected Nonlinearity Using Extreme Learning Machines (published in: International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 21, Suppl. 2 (2013), 117--129.)," Working papers 2013rwp-57, Yonsei University, Yonsei Economics Research Institute.
    • Handle: RePEc:yon:wpaper:2013rwp-57
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    References listed on IDEAS

    as
    1. Jin Seo Cho & Isao Ishida & Halbert White, 2013. "Testing for Neglected Nonlinearity Using Twofold Unidentified Models under the Null and Hexic Expansions (published in: Essays in Nonlinear Time Series Econometrics, Festschrift in Honor of Timo Teras," Working papers 2013rwp-55, Yonsei University, Yonsei Economics Research Institute.
    2. Cho, Jin Seo & White, Halbert, 2010. "Testing for unobserved heterogeneity in exponential and Weibull duration models," Journal of Econometrics, Elsevier, vol. 157(2), pages 458-480, August.
    3. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    4. Jin Seo Cho & Isao Ishida & Halbert White, 2013. "Mathematical Proofs for "Testing for Neglected Nonlinearity Using Twofold Unidentified Models under the Null and Hexic Expansions"," Working papers 2013rwp-55a, Yonsei University, Yonsei Economics Research Institute.
    5. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(3), pages 295-325, June.
    6. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    7. Jin Seo Cho & Halbert White, 2007. "Testing for Regime Switching," Econometrica, Econometric Society, vol. 75(6), pages 1671-1720, November.
    8. Cho, Jin Seo & Ishida, Isao, 2012. "Testing for the effects of omitted power transformations," Economics Letters, Elsevier, vol. 117(1), pages 287-290.
    9. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
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    Keywords

    Extreme learning machines; neglected nonlinearity; Wald test; single layer feedforward network; asymptotic distribution;
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