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Efficiency of linear estimators under heavy-tailedness: convolutions of [alpha]-symmetric distributions

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  • Ibragimov, Rustam

Abstract

This paper focuses on the analysis of efficiency, peakedness, and majorization properties of linear estimators under heavy-tailedness assumptions. We demonstrate that peakedness and majorization properties of log-concavely distributed random samples continue to hold for convolutions of [alpha]-symmetric distributions with [alpha] > 1. However, these properties are reversed in the case of convolutions of [alpha]-symmetric distributions with [alpha]

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  • Ibragimov, Rustam, 2007. "Efficiency of linear estimators under heavy-tailedness: convolutions of [alpha]-symmetric distributions," Scholarly Articles 2623749, Harvard University Department of Economics.
    • Handle: RePEc:hrv:faseco:2623749
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    References listed on IDEAS

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    1. Donald W. K. Andrews, 2005. "Cross-Section Regression with Common Shocks," Econometrica, Econometric Society, vol. 73(5), pages 1551-1585, September.
    2. An, Mark Yuying, 1998. "Logconcavity versus Logconvexity: A Complete Characterization," Journal of Economic Theory, Elsevier, vol. 80(2), pages 350-369, June.
    3. Jensen, D. R., 1997. "Peakedness of linear forms in ensembles and mixtures," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 277-282, October.
    4. Rustam Ibragimov, 2005. "Optimal Bundling Strategies For Complements And Substitutes With Heavy-Tailed Valuations," Harvard Institute of Economic Research Working Papers 2088, Harvard - Institute of Economic Research.
    5. Rustam Ibragimov, 2005. "A Tale of Two Tails: Peakedness Properties in Inheritance Models of Evolutionary Theory," Harvard Institute of Economic Research Working Papers 2092, Harvard - Institute of Economic Research.
    6. Rustam Ibragimov, 2005. "Demand-Driven Innovation and Spatial Competition Over Time Under Heavy-Tailed Signals," Harvard Institute of Economic Research Working Papers 2087, Harvard - Institute of Economic Research.
    7. Rustam Ibragimov, 2005. "Portfolio Diversification and Value at Risk Under Thick-Tailedness," Harvard Institute of Economic Research Working Papers 2086, Harvard - Institute of Economic Research.
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    1. Ankudinov, Andrei & Ibragimov, Rustam & Lebedev, Oleg, 2017. "Sanctions and the Russian stock market," Research in International Business and Finance, Elsevier, vol. 40(C), pages 150-162.
    2. Chen, Zhimin & Ibragimov, Rustam, 2019. "One country, two systems? The heavy-tailedness of Chinese A- and H- share markets," Emerging Markets Review, Elsevier, vol. 38(C), pages 115-141.
    3. Ibragimov Marat & Khamidov Rufat, 2010. "Heavy-Tailedness and Volatility in Emerging Foreign Exchange Markets: Theory and Empirics," EERC Working Paper Series 10/06e, EERC Research Network, Russia and CIS.
    4. Ba, Shusong & Li, Lu & Huang, Wenli & Yang, Chen, 2020. "Heterogeneity risks and negative externality," Economic Modelling, Elsevier, vol. 87(C), pages 401-415.
    5. Ankudinov, Andrei & Ibragimov, Rustam & Lebedev, Oleg, 2017. "Extreme movements of the Russian stock market and their consequences for management and economic modeling," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 45, pages 75-92.
    6. Ju, Shan & Pan, Xiaoqing, 2016. "A new proof for the peakedness of linear combinations of random variables," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 93-98.
    7. Michael Grabchak, 2014. "Does value-at-risk encourage diversification when losses follow tempered stable or more general Lévy processes?," Annals of Finance, Springer, vol. 10(4), pages 553-568, November.
    8. Yuyu Chen & Ruodu Wang, 2024. "Infinite-mean models in risk management: Discussions and recent advances," Papers 2408.08678, arXiv.org, revised Oct 2024.
    9. Ibragimov, Marat & Ibragimov, Rustam & Kattuman, Paul, 2013. "Emerging markets and heavy tails," Journal of Banking & Finance, Elsevier, vol. 37(7), pages 2546-2559.
    10. Ankudinov, Andrei & Ibragimov, Rustam & Lebedev, Oleg, 2017. "Heavy tails and asymmetry of returns in the Russian stock market," Emerging Markets Review, Elsevier, vol. 32(C), pages 200-219.

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