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Efficiency Of Linear Estimators Under Heavy-Tailedness: Convolutions Of Α-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 α-symmetric distributions with α > 1. However, these properties are reversed in the case of convolutions of α-symmetric distributions with α

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  • Ibragimov, Rustam, 2007. "Efficiency Of Linear Estimators Under Heavy-Tailedness: Convolutions Of Α-Symmetric Distributions," Econometric Theory, Cambridge University Press, vol. 23(3), pages 501-517, June.
    • Handle: RePEc:cup:etheor:v:23:y:2007:i:03:p:501-517_07
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Ba, Shusong & Li, Lu & Huang, Wenli & Yang, Chen, 2020. "Heterogeneity risks and negative externality," Economic Modelling, Elsevier, vol. 87(C), pages 401-415.
    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. Rustam Ibragimov & Paul Kattuman & Anton Skrobotov, 2021. "Robust Inference on Income Inequality: $t$-Statistic Based Approaches," Papers 2105.05335, arXiv.org, revised Nov 2021.
    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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