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A martingale-difference-divergence-based test for specification

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  • Su, Liangjun
  • Zheng, Xin

Abstract

In this paper we propose a novel consistent model specification test based on the martingale difference divergence (MDD) of the error term given the covariates. The MDD equals zero if and only if error term is conditionally mean independent of the covariates. Our MDD test does not require any nonparametric estimation under the alternative and it is applicable even if we have many covariates in the regression model. We establish the asymptotic distributions of our test statistic under the null and a sequence of Pitman local alternatives converging to the null at the usual parametric rate. Simulations suggest that our MDD test has superb performance in terms of both size and power and it generally dominates several competitors. In particular, it is the only test that has well controlled size in the presence of many covariates and reasonable power against high frequency alternatives as well.

Suggested Citation

  • Su, Liangjun & Zheng, Xin, 2017. "A martingale-difference-divergence-based test for specification," Economics Letters, Elsevier, vol. 156(C), pages 162-167.
    • Handle: RePEc:eee:ecolet:v:156:y:2017:i:c:p:162-167
    DOI: 10.1016/j.econlet.2017.05.002
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    References listed on IDEAS

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    1. Su, Liangjun & White, Halbert, 2007. "A consistent characteristic function-based test for conditional independence," Journal of Econometrics, Elsevier, vol. 141(2), pages 807-834, December.
    2. Huang, Meng & Sun, Yixiao & White, Halbert, 2016. "A Flexible Nonparametric Test For Conditional Independence," Econometric Theory, Cambridge University Press, vol. 32(6), pages 1434-1482, December.
    3. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
    4. Su, Liangjun & White, Halbert, 2008. "A Nonparametric Hellinger Metric Test For Conditional Independence," Econometric Theory, Cambridge University Press, vol. 24(4), pages 829-864, August.
    5. Su, Liangjun & White, Halbert, 2014. "Testing conditional independence via empirical likelihood," Journal of Econometrics, Elsevier, vol. 182(1), pages 27-44.
    6. Oliver Linton & Pedro Gozalo, 2014. "Testing Conditional Independence Restrictions," Econometric Reviews, Taylor & Francis Journals, vol. 33(5-6), pages 523-552, August.
    7. Runze Li & Wei Zhong & Liping Zhu, 2012. "Feature Screening via Distance Correlation Learning," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1129-1139, September.
    8. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-1458, November.
    9. Fan, Yanqin & Li, Qi, 2000. "Consistent Model Specification Tests," Econometric Theory, Cambridge University Press, vol. 16(6), pages 1016-1041, December.
    10. 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.
    11. Fan, Yanqin, 1998. "Goodness-Of-Fit Tests Based On Kernel Density Estimators With Fixed Smoothing Parameters," Econometric Theory, Cambridge University Press, vol. 14(5), pages 604-621, October.
    12. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
    13. Su, Liangjun & Jin, Sainan & Zhang, Yonghui, 2015. "Specification test for panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 186(1), pages 222-244.
    14. Xiaofeng Shao & Jingsi Zhang, 2014. "Martingale Difference Correlation and Its Use in High-Dimensional Variable Screening," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1302-1318, September.
    15. 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.
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    4. Emmanuel Selorm Tsyawo & Abdul-Nasah Soale, 2021. "A Distance Covariance-based Estimator," Papers 2102.07008, arXiv.org.

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    More about this item

    Keywords

    Distance covariance; Integrated conditional moment test; Martingale difference divergence; Martingale difference correlation; Specification test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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