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Test for model selection using Cramér–von Mises distance in a fixed design regression setting

Author

Listed:
  • Hong Chen

    (University of Hohenheim)

  • Maik Döring

    (University of Hohenheim)

  • Uwe Jensen

    (University of Hohenheim)

Abstract

In this paper a test for model selection is proposed which extends the usual goodness-of-fit test in several ways. It is assumed that the underlying distribution H depends on a covariate value in a fixed design setting. Secondly, instead of one parametric class we consider two competing classes one of which may contain the underlying distribution. The test allows to select one of two equally treated model classes which fits the underlying distribution better. To define the distance of distributions various measures are available. Here the Cramér-von Mises has been chosen. The null hypothesis that both parametric classes have the same distance to the underlying distribution H can be checked by means of a test statistic, the asymptotic properties of which are shown under a set of suitable conditions. The performance of the test is demonstrated by Monte Carlo simulations. Finally, the procedure is applied to a data set from an endurance test on electric motors.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:alstar:v:102:y:2018:i:4:d:10.1007_s10182-017-0317-0
    DOI: 10.1007/s10182-017-0317-0
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    References listed on IDEAS

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    1. Zheng, John Xu, 2000. "A Consistent Test Of Conditional Parametric Distributions," Econometric Theory, Cambridge University Press, vol. 16(5), pages 667-691, October.
    2. Bierens, Herman J. & Wang, Li, 2012. "Integrated Conditional Moment Tests For Parametric Conditional Distributions," Econometric Theory, Cambridge University Press, vol. 28(2), pages 328-362, April.
    3. Qi Li & Juan Lin & Jeffrey S. Racine, 2013. "Optimal Bandwidth Selection for Nonparametric Conditional Distribution and Quantile Functions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 57-65, January.
    4. Christoph Rothe & Dominik Wied, 2013. "Misspecification Testing in a Class of Conditional Distributional Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 314-324, March.
    5. Donald W. K. Andrews, 1997. "A Conditional Kolmogorov Test," Econometrica, Econometric Society, vol. 65(5), pages 1097-1128, September.
    6. Eckhard Liebscher, 2016. "Approximation of distributions by using the Anderson Darling statistic," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(22), pages 6732-6745, November.
    7. 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.
    8. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    9. Bobrowski, Sebastian & Chen, Hong & Döring, Maik & Jensen, Uwe & Schinköthe, Wolfgang, 2015. "Estimation of the lifetime distribution of mechatronic systems in the presence of a covariate: A comparison among parametric, semiparametric and nonparametric models," Reliability Engineering and System Safety, Elsevier, vol. 139(C), pages 105-112.
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