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On uniform confidence intervals for the tail index and the extreme quantile

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  • Sasaki, Yuya
  • Wang, Yulong

Abstract

This paper presents two results concerning uniform confidence intervals for the tail index and the extreme quantile. First, we show that there exists a lower bound of the length for confidence intervals that satisfy the correct uniform coverage over a nonparametric family of tail distributions. Second, in light of the impossibility result, we construct honest confidence intervals that are uniformly valid by incorporating the worst-case bias in the nonparametric family. The proposed method is applied to simulated data and real data of financial time series.

Suggested Citation

  • Sasaki, Yuya & Wang, Yulong, 2024. "On uniform confidence intervals for the tail index and the extreme quantile," Journal of Econometrics, Elsevier, vol. 244(1).
    • Handle: RePEc:eee:econom:v:244:y:2024:i:1:s0304407624002100
    DOI: 10.1016/j.jeconom.2024.105865
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    References listed on IDEAS

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    1. Armelle Guillou & Peter Hall, 2001. "A diagnostic for selecting the threshold in extreme value analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 293-305.
    2. M. Ivette Gomes & Armelle Guillou, 2015. "Extreme Value Theory and Statistics of Univariate Extremes: A Review," International Statistical Review, International Statistical Institute, vol. 83(2), pages 263-292, August.
    3. Xavier Gabaix, 2016. "Power Laws in Economics: An Introduction," Journal of Economic Perspectives, American Economic Association, vol. 30(1), pages 185-206, Winter.
    4. Timothy B. Armstrong & Michal Kolesár, 2018. "Optimal Inference in a Class of Regression Models," Econometrica, Econometric Society, vol. 86(2), pages 655-683, March.
    5. Timothy B. Armstrong & Michal Kolesár, 2020. "Simple and honest confidence intervals in nonparametric regression," Quantitative Economics, Econometric Society, vol. 11(1), pages 1-39, January.
    6. Timothy B Armstrong & Michal Kolesár, 2018. "A Simple Adjustment for Bandwidth Snooping," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(2), pages 732-765.
    7. Kim, Jihyun & Meddahi, Nour, 2020. "Volatility Regressions with Fat Tails," TSE Working Papers 20-1097, Toulouse School of Economics (TSE).
    8. Babii, Andrii, 2020. "Honest Confidence Sets In Nonparametric Iv Regression And Other Ill-Posed Models," Econometric Theory, Cambridge University Press, vol. 36(4), pages 658-706, August.
    9. Xavier Gabaix & Rustam Ibragimov, 2011. "Rank - 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 24-39, January.
    10. Hill, Jonathan B. & Shneyerov, Artyom, 2013. "Are there common values in first-price auctions? A tail-index nonparametric test," Journal of Econometrics, Elsevier, vol. 174(2), pages 144-164.
    11. Gomes, M. Ivette & Pestana, Dinis, 2007. "A Sturdy Reduced-Bias Extreme Quantile (VaR) Estimator," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 280-292, March.
    12. Igor Fedotenkov, 2020. "A Review of More than One Hundred Pareto-Tail Index Estimators," Statistica, Department of Statistics, University of Bologna, vol. 80(3), pages 245-299.
    13. Kim, Jihyun & Meddahi, Nour, 2020. "Volatility regressions with fat tails," Journal of Econometrics, Elsevier, vol. 218(2), pages 690-713.
    14. Hill, Jonathan B., 2010. "On Tail Index Estimation For Dependent, Heterogeneous Data," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1398-1436, October.
    15. Susanne M Schennach, 2020. "A Bias Bound Approach to Non-parametric Inference," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 87(5), pages 2439-2472.
    16. Holger Drees, 1998. "On Smooth Statistical Tail Functionals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 187-210, March.
    17. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    18. Gabaix, Xavier & Ibragimov, Rustam, 2011. "Rank − 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 24-39.
    19. M. Ivette Gomes & Laurens De Haan & Lígia Henriques Rodrigues, 2008. "Tail index estimation for heavy‐tailed models: accommodation of bias in weighted log‐excesses," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 31-52, February.
    20. Yunan Wu & Lan Wang & Haoda Fu, 2023. "Model-Assisted Uniformly Honest Inference for Optimal Treatment Regimes in High Dimension," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(541), pages 305-314, January.
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