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Sequentially Estimating Approximate Conditional Mean Using the Extreme Learning Machine

Author

Listed:
  • LIJUAN HUO

    (Beijing Institute of Technology)

  • JIN SEO CHO

    (Yonsei Univ)

Abstract

This study applies the Wald test statistic assisted by the extreme learning machine (ELM) to test for model misspecification. When testing for model misspecification of conditional mean, the omnibus test statistics weakly converge to a Gaussian stochastic process under the null that makes their application inconvenient. We overcome this by applying the ELM to the Wald test statistic defined by the functional regression and also apply it to a sequential testing procedure to estimate an approximate conditional expectation. By conducting extensive Monte Carlo experiments, we evaluate its performance and verify that the sequential WELM testing procedure estimates the most parsimonious conditional mean equation consistently if the candidate polynomial models are correctly specified; and further it consistently rejects all candidate models if all of them are misspecified.

Suggested Citation

  • Lijuan Huo & Jin Seo Cho, 2020. "Sequentially Estimating Approximate Conditional Mean Using the Extreme Learning Machine," Working papers 2020rwp-180, Yonsei University, Yonsei Economics Research Institute.
    • Handle: RePEc:yon:wpaper:2020rwp-180
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Baek, Yae In & Cho, Jin Seo & Phillips, Peter C.B., 2015. "Testing linearity using power transforms of regressors," Journal of Econometrics, Elsevier, vol. 187(1), pages 376-384.
    4. Lee, Tae-Hwy & White, Halbert & Granger, Clive W. J., 1993. "Testing for neglected nonlinearity in time series models : A comparison of neural network methods and alternative tests," Journal of Econometrics, Elsevier, vol. 56(3), pages 269-290, April.
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    Keywords

    specification testing; conditional mean; omnibus test; Gaussian process; extreme learning machine; sequential testing procedure.;
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