Higher-order expansions for distributions of extremes from general error distribution

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• 作者：Pu Jia (13)
  Tingting Li (13)
  
  13. School of Mathematics and Statistics ; Southwest University ; Chongqing ; 400715 ; P.R. China
  
• 关键词：expansion ; extreme ; general error distribution
• 刊名：Journal of Inequalities and Applications
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：2014
• 期：1
• 全文大小：176 KB
• 参考文献：1. Nelson, DB (1991) Conditional heteroskedasticity in asset returns: a new approach. Econometrica 59: pp. 347-370 CrossRef
  2. Leadbetter, MR, Lindgren, G, Rootz茅n, H (1983) Extremes and Related Properties of Random Sequences and Processes. Springer, New York CrossRef
  3. Resnick, SI (1987) Extreme Values, Regular Variation and Point Processes. Springer, New York CrossRef
  4. Peng, Z, Tong, B, Nadarajah, S (2009) Tail behavior of the general error distribution. Econometrica 38: pp. 1884-1892
  5. Hall, P (1979) On the rate of convergence of normal extremes. J. Appl. Probab 16: pp. 433-439 CrossRef
  6. Peng, Z, Nadarajah, S, Lin, F (2010) Convergence rate of extremes for the general error distribution. J. Appl. Probab 47: pp. 668-679 CrossRef
  7. Nair, KA (1981) Asymptotic distribution and moments of normal extremes. Stat. Probab. Lett 9: pp. 150-153
  8. Liao, X, Peng, Z (2012) Convergence rate of limit distribution of maxima of lognormal samples. J. Math. Anal. Appl 395: pp. 643-653 CrossRef
  9. Liao, X, Peng, Z, Nadarajah, S (2013) Tail properties and asymptotic expansions for the maximum of logarithmic skew-normal distribution. J. Appl. Probab 50: pp. 900-907 CrossRef
  10. Liao, X, Peng, Z, Nadarajah, S, Wang, X (2014) Rates of convergence of extremes from skew normal sample. Stat. Probab. Lett 84: pp. 40-47 CrossRef
  
• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X

文摘

In this short note, with optimal normalizing constants, the higher-order expansion for a distribution of normalized partial maximum from the general error distribution is derived, by which one deduces the associate convergence rate of the distribution of the extreme to the Gumbel extreme value distribution. MSC: 62E20, 60E05, 60F15, 60G15.