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Rates of convergence of extremes from skew-normal samples

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  • Liao, Xin
  • Peng, Zuoxiang
  • Nadarajah, Saralees
  • Wang, Xiaoqian

Abstract

For a skew-normal random sequence, convergence rates of the distribution of its partial maximum to the Gumbel extreme value distribution are derived. The asymptotic expansion of the distribution of the normalized maximum is given under an optimal choice of norming constants. We find that the optimal convergence rate of the normalized maximum to the Gumbel extreme value distribution is proportional to 1/logn.

Suggested Citation

  • Liao, Xin & Peng, Zuoxiang & Nadarajah, Saralees & Wang, Xiaoqian, 2014. "Rates of convergence of extremes from skew-normal samples," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 40-47.
    • Handle: RePEc:eee:stapro:v:84:y:2014:i:c:p:40-47
    DOI: 10.1016/j.spl.2013.09.027
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    References listed on IDEAS

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    1. Maximiano Pinheiro & Paulo Esteves, 2012. "On the uncertainty and risks of macroeconomic forecasts: combining judgements with sample and model information," Empirical Economics, Springer, vol. 42(3), pages 639-665, June.
    2. Sáez, Antonio José & Prieto, Faustino & Sarabia, José María, 2012. "A two-tail version of the PPS distribution with application to current account balance data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(21), pages 5160-5171.
    3. Marjan Mansourian & Anoshirvan Kazemnejad & Iraj Kazemi & Farid Zayeri & Masoud Soheilian, 2012. "Bayesian analysis of longitudinal ordered data with flexible random effects using McMC: application to diabetic macular Edema data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(5), pages 1087-1100, November.
    4. Chen, Shouquan & Wang, Chao & Zhang, Geng, 2012. "Rates of convergence of extreme for general error distribution under power normalization," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 385-395.
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    Cited by:

    1. Xiong, Qian & Peng, Zuoxiang, 2020. "Asymptotic expansions of powered skew-normal extremes," Statistics & Probability Letters, Elsevier, vol. 158(C).
    2. Rendao Ye & Bingni Fang & Weixiao Du & Kun Luo & Yiting Lu, 2022. "Bootstrap Tests for the Location Parameter under the Skew-Normal Population with Unknown Scale Parameter and Skewness Parameter," Mathematics, MDPI, vol. 10(6), pages 1-23, March.
    3. Beranger, B. & Padoan, S.A. & Xu, Y. & Sisson, S.A., 2019. "Extremal properties of the univariate extended skew-normal distribution, Part A," Statistics & Probability Letters, Elsevier, vol. 147(C), pages 73-82.
    4. Beranger, B. & Padoan, S.A. & Xu, Y. & Sisson, S.A., 2019. "Extremal properties of the multivariate extended skew-normal distribution, Part B," Statistics & Probability Letters, Elsevier, vol. 147(C), pages 105-114.
    5. Sha Jiang & Tingting Li & Xin Liao, 2018. "Distributional expansions on extremes from skew-normal distribution under power normalization," Statistical Papers, Springer, vol. 59(1), pages 1-20, March.

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