Rates of convergence of extremes from skew-normal samples

By Xin Liao, Zuoxiang Peng, Saralees Nadarajah, Xiao-qian Wang. 2012

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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.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/af9e635696d2df6c564f4253ecbfbc163db7900c