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A Nonparametric Bootstrap Test Of Conditional Distributions

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  • Fan, Yanqin
  • Li, Qi
  • Min, Insik

Abstract

This paper proposes a bootstrap test for the correct specification of parametric conditional distributions. It extends Zheng's test (Zheng, 2000, Econometric Theory 16, 667–691) to allow for discrete dependent variables and for mixed discrete and continuous conditional variables. We establish the asymptotic null distribution of the test statistic with data-driven stochastic smoothing parameters. By smoothing both the discrete and continuous variables via the method of cross-validation, our test has the advantage of automatically removing irrelevant variables from the estimate of the conditional density function and, as a consequence, enjoys substantial power gains in finite samples, as confirmed by our simulation results. The simulation results also reveal that the bootstrap test successfully overcomes the size distortion problem associated with Zheng's test.We are grateful for the insightful comments from three referees and a co-editor that greatly improved the paper. Li's research is partially supported by the Private Enterprise Research Center, Texas A&M University. Fan is grateful to the National Science Foundation for research support.

Suggested Citation

  • Fan, Yanqin & Li, Qi & Min, Insik, 2006. "A Nonparametric Bootstrap Test Of Conditional Distributions," Econometric Theory, Cambridge University Press, vol. 22(4), pages 587-613, August.
    • Handle: RePEc:cup:etheor:v:22:y:2006:i:04:p:587-613_06
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    1. repec:wyi:journl:002117 is not listed on IDEAS
    2. Huang, Ta-Cheng & Li, Hongjun & Li, Zheng, 2020. "A modified bootstrap for kernel-based specification test with heavy-tailed data," Economics Letters, Elsevier, vol. 189(C).
    3. Obbey Elamin & Len Gill & Martyn Andrews, 2020. "Insights from kernel conditional-probability estimates into female labour force participation decision in the UK," Empirical Economics, Springer, vol. 58(6), pages 2981-3006, June.
    4. repec:wyi:journl:002142 is not listed on IDEAS
    5. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    6. Chen, Bin & Hong, Yongmiao, 2014. "A unified approach to validating univariate and multivariate conditional distribution models in time series," Journal of Econometrics, Elsevier, vol. 178(P1), pages 22-44.
    7. Chen, Bin & Hong, Yongmiao, 2012. "Testing For The Markov Property In Time Series," Econometric Theory, Cambridge University Press, vol. 28(1), pages 130-178, February.
    8. Chen, Bin & Hong, Yongmiao, 2016. "Detecting For Smooth Structural Changes In Garch Models," Econometric Theory, Cambridge University Press, vol. 32(03), pages 740-791, June.
    9. Chauvet, Marcelle & Tierney, Heather L. R., 2007. "Real Time Changes in Monetary Policy," MPRA Paper 16199, University Library of Munich, Germany, revised Apr 2009.
    10. Henderson, Daniel J. & Parmeter, Christopher F., 2015. "A consistent bootstrap procedure for nonparametric symmetry tests," Economics Letters, Elsevier, vol. 131(C), pages 78-82.

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