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Rearranging Edgeworth–Cornish–Fisher expansions

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  • Victor Chernozhukov
  • Iván Fernández-Val
  • Alfred Galichon

Abstract

This paper applies a regularization procedure called increasing rearrangement to monotonize Edgeworth and Cornish-Fisher expansions and any other related approximations of distribution and quantile functions of sample statistics. Besides satisfying the logical monotonicity, required of distribution and quantile functions, the procedure often delivers strikingly better approximations to the distribution and quantile functions of the sample mean than the original Edgeworth-Cornish-Fisher expansions.
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Suggested Citation

  • Victor Chernozhukov & Iván Fernández-Val & Alfred Galichon, 2010. "Rearranging Edgeworth–Cornish–Fisher expansions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 419-435, February.
    • Handle: RePEc:spr:joecth:v:42:y:2010:i:2:p:419-435
    DOI: 10.1007/s00199-008-0431-z
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    References listed on IDEAS

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    1. Rothenberg, Thomas J., 1984. "Approximating the distributions of econometric estimators and test statistics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 15, pages 881-935, Elsevier.
    2. Sargan, J D, 1976. "Econometric Estimators and the Edgeworth Approximation," Econometrica, Econometric Society, vol. 44(3), pages 421-448, May.
    3. Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007. "Improving Estimates Of Monotone Functions By Rearrangement," Boston University - Department of Economics - Working Papers Series WP2007-012, Boston University - Department of Economics.
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    Cited by:

    1. Candelon, Bertrand & Fuerst, Franz & Hasse, Jean-Baptiste, 2021. "Diversification potential in real estate portfolios," International Economics, Elsevier, vol. 166(C), pages 126-139.
    2. Brenda Castillo-Brais & Ángel León & Juan Mora, 2022. "Estimating Value-at-Risk and Expected Shortfall: Do Polynomial Expansions Outperform Parametric Densities?," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
    3. Charles-Olivier Amedee-Manesme & Fabrice Barthélémy, 2012. "Cornish-Fisher expansion for real estate value at risk," ERES eres2012_044, European Real Estate Society (ERES).
    4. Donald Lien & Christopher Stroud & Keying Ye, 2013. "Comparing VaR Approximation Methods Which Use the First Four Moments as Inputs," Working Papers 0220mss, College of Business, University of Texas at San Antonio.
    5. Giuseppe De Luca & Jan R. Magnus & Franco Peracchi, 2021. "Posterior moments and quantiles for the normal location model with Laplace prior," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(17), pages 4039-4049, August.
    6. Ghossoub, Mario, 2011. "Monotone equimeasurable rearrangements with non-additive probabilities," MPRA Paper 37629, University Library of Munich, Germany, revised 23 Mar 2012.
    7. Liu, Nianqing & Vuong, Quang & Xu, Haiqing, 2017. "Rationalization and identification of binary games with correlated types," Journal of Econometrics, Elsevier, vol. 201(2), pages 249-268.
    8. Charles-Olivier Amédée-Manesme & Fabrice Barthélémy & Didier Maillard, 2019. "Computation of the corrected Cornish–Fisher expansion using the response surface methodology: application to VaR and CVaR," Annals of Operations Research, Springer, vol. 281(1), pages 423-453, October.
    9. Victor Chernozhukov & Pierre-André Chiappori & Marc Henry, 2010. "Introduction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 271-273, February.
    10. Charles-Olivier Amédée-Manesme & Fabrice Barthélémy, 2022. "Proper use of the modified Sharpe ratios in performance measurement: rearranging the Cornish Fisher expansion," Annals of Operations Research, Springer, vol. 313(2), pages 691-712, June.
    11. Charles-Olivier Amédée-Manesme & Fabrice Barthélémy & Donald Keenan, 2015. "Cornish-Fisher Expansion for Commercial Real Estate Value at Risk," The Journal of Real Estate Finance and Economics, Springer, vol. 50(4), pages 439-464, May.
    12. Charles-Olivier Amédée-Manesme & Fabrice Barthélémy & Jean-Luc Prigent & Donald Keenan & Mahdi Mokrane, 2017. "Modified Sharpe Ratios in Real Estate Performance Measurement: Beyond the Standard Cornish Fisher Expansion," THEMA Working Papers 2017-20, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    13. Stéphane Hamayon & Florence Legros & Pradat Yannick, 2016. "Non gaussian returns: which impact on default options retirement plans? [Distribution non gaussienne des rendements : quel impact sur les options par défaut des plans d'épargne retraite ?]," Working Papers hal-03003588, HAL.
    14. Karlygash Kurlbayeva & Samuel Malone, 2012. "The determinants of extreme commodity prices," OxCarre Working Papers 096, Oxford Centre for the Analysis of Resource Rich Economies, University of Oxford.
    15. Lee, Wing Yan & Li, Xiaolong & Liu, Fangda & Shi, Yifan & Yam, Sheung Chi Phillip, 2021. "A Fourier-cosine method for finite-time ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 256-267.
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    17. Carnero, M. Angeles & León, Angel & Ñíguez, Trino-Manuel, 2023. "Skewness in energy returns: estimation, testing and retain-->implications for tail risk," The Quarterly Review of Economics and Finance, Elsevier, vol. 90(C), pages 178-189.

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    More about this item

    Keywords

    Edgeworth expansion; Cornish–Fisher expansion; Rearrangement; Higher order central limit theorem; D10; C50;
    All these keywords.

    JEL classification:

    • D10 - Microeconomics - - Household Behavior - - - General
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General

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