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Goodness-of-fit testing in regression: A finite sample comparison of bootstrap methodology and Khmaladze transformation

Author

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  • Koul, Hira L.
  • Sakhanenko, Lyudmila

Abstract

It is well known that the tests based on the residual empirical process for fitting an error distribution in regression models are not asymptotically distribution free. One either uses a Monte-Carlo method or a bootstrap method to implement them. Another option is to base tests on the Khmaladze transformation of these processes because it renders them asymptotically distribution free. This note compares Monte-Carlo, naive bootstrap, and the smooth bootstrap methods of implementing the Kolmogorov-Smirnov test with the Khmaladze transformed test. We find that the transformed test outperforms the naive and smooth bootstrap methods in preserving the level. The note also includes a power comparison of these tests.

Suggested Citation

  • Koul, Hira L. & Sakhanenko, Lyudmila, 2005. "Goodness-of-fit testing in regression: A finite sample comparison of bootstrap methodology and Khmaladze transformation," Statistics & Probability Letters, Elsevier, vol. 74(3), pages 290-302, October.
    • Handle: RePEc:eee:stapro:v:74:y:2005:i:3:p:290-302
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    Citations

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    Cited by:

    1. Jiwoong Kim, 2020. "Implementation of a goodness-of-fit test through Khmaladze martingale transformation," Computational Statistics, Springer, vol. 35(4), pages 1993-2017, December.
    2. Feng, Huijun & Peng, Liang, 2012. "Jackknife empirical likelihood tests for error distributions in regression models," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 63-75.
    3. Juan Mora & Alicia Pérez-Alonso, 2009. "Specification tests for the distribution of errors in nonparametric regression: a martingale approach," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(4), pages 441-452.
    4. Sam Efromovich, 2010. "Oracle inequality for conditional density estimation and an actuarial example," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(2), pages 249-275, April.
    5. Parker, Thomas, 2010. "A comparison of alternative approaches to sup-norm goodness of git gests with estimated parameters," MPRA Paper 22926, University Library of Munich, Germany.

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