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A comparison of alternative approaches to sup-norm goodness of fit tests with estimated parameters

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  • Thomas Parker

    (Institute for Fiscal Studies)

Abstract

Goodness of fit tests based on sup-norm statistics of empirical processes have nonstandard limiting distributions when the null hypothesis is composite-that is, when parameters of the null model are estimated. Several solutions to this problem have been suggested, including the calculation of adjusted critical values for these nonstandard distributions and the transformation of the empirical process such that statistics based on the transformed process are asymptotically distribution-free. The approximation methods proposed by Durbin (1985) can be applied to compute appropriate critical values for tests based on sup-norm statistics. The resulting tests have quite accurate size, a fact which has gone unrecognized in the econometrics literature. Some justification for this accuracy lies in the similar features that Durbin's approximation methods share with the theory of extrema for Gaussian random fields and for Gauss-Markov processes. These adjustment techniques are also related to the transformation methodology proposed by Khmaladze (1981) through the score function of the parametric model. Monte Carlo experiments suggest that these two testing strategies are roughly comparable to one another and more powerful than a simple bootstrap procedure.

Suggested Citation

  • Thomas Parker, 2010. "A comparison of alternative approaches to sup-norm goodness of fit tests with estimated parameters," CeMMAP working papers CWP34/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:34/10
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    File URL: http://cemmap.ifs.org.uk/wps/cwp3410.pdf
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    References listed on IDEAS

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    1. Muneya Matsui & Akimichi Takemura, 2005. "Empirical characteristic function approach to goodness-of-fit tests for the Cauchy distribution with parameters estimated by MLE or EISE," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(1), pages 183-199, March.
    2. 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.
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    6. Jushan Bai, 2003. "Testing Parametric Conditional Distributions of Dynamic Models," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 531-549, August.
    7. Roger Koenker & Zhijie Xiao, 2002. "Inference on the Quantile Regression Process," Econometrica, Econometric Society, vol. 70(4), pages 1583-1612, July.
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    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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