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极值指数估计与高分位数估计AI 解读

This paper consists of two parts. An easy proof is given for the weak consistency of Pickands' estimate for the main parameter of an extreme-value distribution. Moreover, further natural conditions are given for strong consistency and for asymptotic normality of the estimate. Next a large quantile of a distribution is estimated by a combination of extreme or intermediate order statistics. This leads to an asymptotic confidence interval.

正则变化分布函数下的样本分位数AI 解读

A law of the iterated logarithm is proved for sample $p$-quantiles when the probability distribution function varies regularly at $\\xi$ with $F(\\xi) = p$.