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A Consistent Test Of Conditional Parametric Distributions

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  • Zheng, John Xu

Abstract

This paper proposes a new nonparametric test for conditional parametric distribution functions based on the first-order linear expansion of the Kullback–Leibler information function and the kernel estimation of the underlying distributions. The test statistic is shown to be asymptotically distributed standard normal under the null hypothesis that the parametric distribution is correctly specified, whereas asymptotically rejecting the null with probability one if the parametric distribution is misspecified. The test is also shown to have power against any local alternatives approaching the null at rates slower than the parametric rate n−1/2. The finite sample performance of the test is evaluated via a Monte Carlo simulation.

Suggested Citation

  • Zheng, John Xu, 2000. "A Consistent Test Of Conditional Parametric Distributions," Econometric Theory, Cambridge University Press, vol. 16(5), pages 667-691, October.
    • Handle: RePEc:cup:etheor:v:16:y:2000:i:05:p:667-691_16
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    Citations

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    Cited by:

    1. Marcelo Fernandes & Breno Neri, 2010. "Nonparametric Entropy-Based Tests of Independence Between Stochastic Processes," Econometric Reviews, Taylor & Francis Journals, vol. 29(3), pages 276-306.
    2. Fuchun Li & Greg Tkacz, 2001. "A Consistent Bootstrap Test for Conditional Density Functions with Time-Dependent Data," Staff Working Papers 01-21, Bank of Canada.
    3. Juan Mora & Antonia Febrer, 2005. "Wage Distribution In Spain, 1994-1999: An Application Of A Flexible Estimator Of Conditional Distributions," Working Papers. Serie EC 2005-04, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    4. Delgado, Miguel A. & Stute, Winfried, 2008. "Distribution-free specification tests of conditional models," Journal of Econometrics, Elsevier, vol. 143(1), pages 37-55, March.
    5. Li, Fuchun & Tkacz, Greg, 2006. "A consistent bootstrap test for conditional density functions with time-series data," Journal of Econometrics, Elsevier, vol. 133(2), pages 863-886, August.
    6. 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.
    7. Li, Yong & Yu, Jun & Zeng, Tao, 2018. "Specification tests based on MCMC output," Journal of Econometrics, Elsevier, vol. 207(1), pages 237-260.
    8. Xu Zheng, 2012. "Testing parametric conditional distributions using the nonparametric smoothing method," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(4), pages 455-469, May.
    9. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    10. Stefania D'Amico, 2004. "Density Estimation and Combination under Model Ambiguity," Computing in Economics and Finance 2004 273, Society for Computational Economics.
    11. 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.
    12. Clements, Michael P. & Franses, Philip Hans & Swanson, Norman R., 2004. "Forecasting economic and financial time-series with non-linear models," International Journal of Forecasting, Elsevier, vol. 20(2), pages 169-183.
    13. Febrer, Antonia & Mora, Juan, 2009. "Flexible estimation of wage distributions in the presence of covariates," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2189-2200, April.
    14. Eduardo Fé, 2013. "Estimating production frontiers and efficiency when output is a discretely distributed economic bad," Journal of Productivity Analysis, Springer, vol. 39(3), pages 285-302, June.
    15. Hong Chen & Maik Döring & Uwe Jensen, 2018. "Test for model selection using Cramér–von Mises distance in a fixed design regression setting," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(4), pages 505-535, October.
    16. Cui Rui & Li Yuhao, 2024. "Goodness-of-Fit for Conditional Distributions: An Approach Using Principal Component Analysis and Component Selection," Papers 2403.10352, arXiv.org.
    17. Derumigny Alexis & Fermanian Jean-David, 2017. "About tests of the “simplifying” assumption for conditional copulas," Dependence Modeling, De Gruyter, vol. 5(1), pages 154-197, August.
    18. Zheng, Xu, 2008. "Testing for discrete choice models," Economics Letters, Elsevier, vol. 98(2), pages 176-184, February.
    19. Wu, Edmond H.C. & Yu, Philip L.H. & Li, W.K., 2009. "A smoothed bootstrap test for independence based on mutual information," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2524-2536, May.
    20. Stefania D'Amico, 2005. "Density selection and combination under model ambiguity: an application to stock returns," Finance and Economics Discussion Series 2005-09, Board of Governors of the Federal Reserve System (U.S.).

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