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Articles

Rates of convergence of powered order statistics from general error distribution

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Pages 1-29 | Received 03 May 2020, Accepted 04 Nov 2022, Published online: 21 Nov 2022

References

  • Cao, W., & Zhang, Z. (2021). New extreme value theory for maxima of maxima. Statistical Theory and Related Fields, 5(3), 232–252. https://doi.org/10.1080/24754269.2020.1846115
  • Hall, P. (1979). On the rate of convergence of normal extremes. Journal of Applied Probability, 16(2), 433–439. https://doi.org/10.2307/3212912
  • Hall, P. (1980). Estimating probabilities for normal extremes. Advances in Applied Probability, 12(2), 491–500. https://doi.org/10.2307/1426608
  • Hashorva, E., Peng, Z., & Weng, Z. (2016). Higher-order expansions of distributions of maxima in a Hüsler-Reiss model. Methodology and Computing in Applied Probability, 18(1), 181–196. https://doi.org/10.1007/s11009-014-9407-6
  • Jia, P., & Li, T. (2014). Higher-order expansions for distributions of extremes from general error distribution. Journal of Inequalities and Applications, 2014, 213. https://doi.org/10.1186/1029-242X-2014-213
  • Leadbetter, M. R., Lindgren, G., & Rootzén, H. (1983). Extremes and related properties of random sequences and processes. Springer Verlag.
  • Li, T., & Peng, Z. (2018). Moment convergence of powered normal extremes. Communication in Statistics-Theory and Methods, 47(14), 3453–3463. https://doi.org/10.1080/03610926.2017.1359294
  • Liao, X., Peng, L., Peng, Z., & Zheng, Y. (2016). Dynamic bivariate normal copula. Science China Mathematics, 59(5), 955–976. https://doi.org/10.1007/s11425-015-5114-1
  • Liao, X., & Peng, Z. (2012). Convergence rates of limit distribution of maxima of lognormal samples. Journal of Mathematical Analysis and Applications, 395(2), 643–653. https://doi.org/10.1016/j.jmaa.2012.05.077
  • Liao, X., & Peng, Z. (2014). Convergence rate of maxima of bivariate gaussian arrays to the Hüsler–Reiss distribution. Statistics and Its Interface, 7(3), 351–362. https://doi.org/10.4310/SII.2014.v7.n3.a5
  • Liao, X., & Peng, Z. (2015). Asymptotics for the maxima and minima of Hüsler–Reiss bivariate gaussian arrays. Extremes, 18, 1–14. https://doi.org/10.1007/s10687-014-0196-7
  • Liao, X., Peng, Z., & Nadarajah, S. (2014a). Tail behavior and limit distribution of maximum of logarithmic general error distribution. Communications in Statistics-Theory and Methods, 43(24), 5276–5289. https://doi.org/10.1080/03610926.2012.730168
  • Liao, X., Peng, Z., Nadarajah, S., & Wang, X. (2014b, January). Rates of convergence of extremes from skew-normal samples. Statistics and Probability Letters, 84, 40–47. https://doi.org/10.1016/j.spl.2013.09.027
  • Lu, Y., & Peng, Z. (2017). Maxima and minima of independent and non-identically distributed bivariate Gaussian triangular arrays. Extremes, 20, 187–198. https://doi.org/10.1007/s10687-016-0263-3
  • Nair, K. A. (1981). Asymptotic distribution and moments of normal extremes. Annals of Probability, 9(1), 150–153. https://doi.org/10.1214/aop/1176994515
  • Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59(2), 347–370. https://doi.org/10.2307/2938260
  • Peng, Z., Nadarajah, S., & Lin, F. (2010). Convergence rate of extremes for the general error distribution. Journal of Applied Probability, 47(3), 668–679. https://doi.org/10.1239/jap/1285335402
  • Peng, Z., Tong, B., & Nadarajah, S. (2009). Tail behavior of the general error distribution. Communications in Statistics-Thoery and Methods, 38(11), 1884–1892. https://doi.org/10.1080/03610920802478367
  • Resnick, S. I. (1987). Extreme values, regular variation and point processes. Springer-Verlag.
  • Zhang, Z. (2021). On studying extreme values and systematic risks with nonlinear time series models and tail dependence measures. Statistical Theory and Related Fields, 5(1), 1–25. https://doi.org/10.1080/24754269.2020.1856590
  • Zhou, W., & Ling, C. (2016, April). Higher-order expansions of powered extremes of normal samples. Statistics and Probability Letters, 111, 12–17. https://doi.org/10.1016/j.spl.2016.01.003