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Asymptotically Distribution-Free Goodness-of-Fit Testing: A Unifying View

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  • Bo Li

Abstract

We outline a general paradigm for constructing asymptotically distribution-free (ADF) goodness-of-fit tests, which can be regarded as a generalization of Khmaladze (1993). This is achieved by a nonorthogonal projection of a class of functions onto the ortho-complement of the extended tangent space (ETS) associated with the null hypothesis. In parallel with the work of Bickel et al. (2006), we obtain transformed empirical processes (TEP) which are the building blocks for constructing omnibus tests such as the usual Kolmogorov-Smirnov type tests and Cramer-von Mise type tests, as well as Portmanteau tests and directional tests. The critical values can be tabulated due to the ADF property. All the tests are capable of detecting local (Pitman) alternative at the root-n scale. We shall illustrate the framework in several examples, mostly in regression model specification testing.

Suggested Citation

  • Bo Li, 2009. "Asymptotically Distribution-Free Goodness-of-Fit Testing: A Unifying View," Econometric Reviews, Taylor & Francis Journals, vol. 28(6), pages 632-657.
    • Handle: RePEc:taf:emetrv:v:28:y:2009:i:6:p:632-657
    DOI: 10.1080/07474930903038933
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    Cited by:

    1. Chen, Qiang & Zheng, Xu & Pan, Zhiyuan, 2015. "Asymptotically distribution-free tests for the volatility function of a diffusion," Journal of Econometrics, Elsevier, vol. 184(1), pages 124-144.
    2. Bontemps, Christian, 2014. "Simple moment-based tests for value-at-risk models and discrete distribution," TSE Working Papers 14-535, Toulouse School of Economics (TSE).
    3. Chung, EunYi & Olivares, Mauricio, 2021. "Permutation test for heterogeneous treatment effects with a nuisance parameter," Journal of Econometrics, Elsevier, vol. 225(2), pages 148-174.
    4. Bontemps, Christian, 2013. "Moment-Based Tests for Discrete Distributions," IDEI Working Papers 772, Institut d'Économie Industrielle (IDEI), Toulouse, revised Oct 2014.
    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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