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Valid Locally Uniform Edgeworth Expansions Under Weak Dependence and Sequences of Smooth Transformations

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  • Stelios Arvanitis

    ()

  • Antonis Demos

    ()
    (www.aueb.gr/users/demos)

Abstract

In this paper we are concerned with the issue of the existence of locally uniform Edgeworth expansions for the distributions of parameterized random vectors. Our motivation resides on the fact that this could enable subsequent polynomial asymptotic expansions of moments. These could be useful for the establishment of asymptotic properties for estimators based on these moments. We derive sufficient conditions either in the case of stochastic processes exhibiting weak dependence, or in the case of smooth transformations of such expansions.

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File URL: http://wpa.deos.aueb.gr/docs/Unif-Edg-fin-wp.pdf
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Bibliographic Info

Paper provided by Athens University of Economics and Business in its series DEOS Working Papers with number 1229.

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Length: 48 pages
Date of creation: 05 Jun 2012
Date of revision: 24 Aug 2012
Handle: RePEc:aue:wpaper:1229

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Related research

Keywords: Locally uniform Edgeworth expansion; formal Edgeworth distribution; weak dependence; smooth transformations; moment approximations; GMM estimators; Indirect estimators; GARCH model;

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References

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  1. Corradi, Valentina & Iglesias, Emma M., 2008. "Bootstrap refinements for QML estimators of the GARCH(1,1) parameters," Journal of Econometrics, Elsevier, vol. 144(2), pages 500-510, June.
  2. Antonis Demos & Stelios Arvanitis, 2010. "Stochastic Expansions and Moment Approximations for Three Indirect Estimators," DEOS Working Papers 1004, Athens University of Economics and Business.
  3. Gourieroux, C. & Monfort, A. & Renault, E., 1992. "Indirect Inference," Papers 92.279, Toulouse - GREMAQ.
  4. Magdalinos, Michael A., 1992. "Stochastic Expansions and Asymptotic Approximations," Econometric Theory, Cambridge University Press, vol. 8(03), pages 343-367, September.
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Cited by:
  1. Stelios Arvanitis & Antonis Demos, . "On the Validity of Edgeworth Expansions and Moment Approximations for Three Indirect Estimators (Extended Revised Appendix)," DEOS Working Papers 1330, Athens University of Economics and Business, revised 28 Jun 2013.
  2. Antonis Demos & Stelios Arvanitis, 2012. "Stochastic Expansions and Moment Approximations for Three Indirect Estimators Revised (Extended Appendix)," DEOS Working Papers 1215, Athens University of Economics and Business.

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