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Stochastic Expansions and Asymptotic Approximations

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  • Magdalinos, Michael A.

Abstract

Under general conditions the distribution function of the first few terms in a stochastic expansion of an econometric estimator or test statistic provides an asymptotic approximation to the distribution function of the original estimator or test statistic with an error of order less than that of the limiting normal or chi-square approximation. This can be used to establish the validity of several refined asymptotic methods, including the comparison of Nagar-type moments and the use of formal Edgeworth or Edgeworth-type approximations.

Suggested Citation

  • Magdalinos, Michael A., 1992. "Stochastic Expansions and Asymptotic Approximations," Econometric Theory, Cambridge University Press, vol. 8(3), pages 343-367, September.
    • Handle: RePEc:cup:etheor:v:8:y:1992:i:03:p:343-367_01
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    Cited by:

    1. Arvanitis Stelios & Demos Antonis, 2018. "On the Validity of Edgeworth Expansions and Moment Approximations for Three Indirect Inference Estimators," Journal of Econometric Methods, De Gruyter, vol. 7(1), pages 1-38, January.
    2. Hwang, Jungbin & Kang, Byunghoon & Lee, Seojeong, 2022. "A doubly corrected robust variance estimator for linear GMM," Journal of Econometrics, Elsevier, vol. 229(2), pages 276-298.
    3. Symeonides Spyridon D. & Karavias Yiannis & Tzavalis Elias, 2017. "Size corrected Significance Tests in Seemingly Unrelated Regressions with Autocorrelated Errors," Journal of Time Series Econometrics, De Gruyter, vol. 9(1), pages 1-41, January.
    4. Stelios Arvanitis & Antonis Demos, 2015. "A class of indirect inference estimators: higher‐order asymptotics and approximate bias correction," Econometrics Journal, Royal Economic Society, vol. 18(2), pages 200-241, June.
    5. Magdalinos, Michael A. & Symeonides, Spyridon D., 1995. "Alternative size corrections for some GLS test statistics the case of the AR(1) model," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 35-59.
    6. Kakizawa, Yoshihide, 2015. "Third-order local power properties of tests for a composite hypothesis, II," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 99-112.
    7. Daniel Wilhelm, 2014. "Optimal bandwidth selection for robust generalized method of moments estimation," CeMMAP working papers 15/14, Institute for Fiscal Studies.
    8. Wilhelm, Daniel, 2015. "Optimal Bandwidth Selection For Robust Generalized Method Of Moments Estimation," Econometric Theory, Cambridge University Press, vol. 31(5), pages 1054-1077, October.
    9. Antonis Demos & Stelios Arvanitis, 2010. "Stochastic Expansions and Moment Approximations for Three Indirect Estimators," DEOS Working Papers 1004, Athens University of Economics and Business.
    10. Kakizawa, Yoshihide, 2017. "Third-order average local powers of Bartlett-type adjusted tests: Ordinary versus adjusted profile likelihood," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 98-120.
    11. Antonis Demos & Stelios Arvanitis, 2012. "On the Validity of Edgeworth Expansions and Moment Approximations for Three Indirect Estimators (Extended Revised Appendix)," DEOS Working Papers 1230, Athens University of Economics and Business.
    12. Antonis Demos & Stelios Arvanitis, 2010. "Stochastic Expansions and Moment Approximations for Three Indirect Estimators," DEOS Working Papers 1004, Athens University of Economics and Business.
    13. Kakizawa, Yoshihide, 2012. "Generalized Cordeiro–Ferrari Bartlett-type adjustment," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 2008-2016.
    14. Kakizawa, Yoshihide, 2009. "Third-order power comparisons for a class of tests for multivariate linear hypothesis under general distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 473-496, March.
    15. 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.
    16. Antonis Demos & Stelios Arvanitis, 2010. "A New Class of Indirect Estimators and Bias Correction," DEOS Working Papers 1023, Athens University of Economics and Business.
    17. Karavias, Yiannis & Symeonides, Spyridon D. & Tzavalis, Elias, 2018. "Higher order expansions for error variance matrix estimates in the Gaussian AR(1) linear regression model," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 54-59.
    18. Stelios Arvanitis & Antonis Demos, 2012. "Valid Locally Uniform Edgeworth Expansions Under Weak Dependence and Sequences of Smooth Transformations," DEOS Working Papers 1229, Athens University of Economics and Business, revised 24 Aug 2012.
    19. Magdalinos, Michael A. & Symeonides, Spyridon D., 1996. "A reinterpretation of the tests of overidentifying restrictions," Journal of Econometrics, Elsevier, vol. 73(2), pages 325-353, August.
    20. Kakizawa, Yoshihide & Iwashita, Toshiya, 2008. "A comparison of higher-order local powers of a class of one-way MANOVA tests under general distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1128-1153, July.
    21. repec:aue:wpaper:1214 is not listed on IDEAS
    22. Kakizawa, Yoshihide, 2010. "Comparison of Bartlett-type adjusted tests in the multiparameter case," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1638-1655, August.
    23. Kakizawa, Yoshihide, 2013. "Third-order local power properties of tests for a composite hypothesis," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 303-317.
    24. Cribari-Netoa, Francisco & Ferrari, Silvia L. P., 1995. "Bartlett-corrected tests for heteroskedastic linear models," Economics Letters, Elsevier, vol. 48(2), pages 113-118, May.
    25. Kakizawa, Yoshihide, 2012. "Improved chi-squared tests for a composite hypothesis," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 141-161.

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