异构幂律数据的极值推断

IF 3.2 1区 数学 Q1 STATISTICS & PROBABILITY
John H.J. Einmahl, Yi He
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引用次数: 0

摘要

我们将极值统计扩展到具有可能非常不同分布的独立数据。特别地,我们给出了Hill估计量的新的渐近正态性结果,它现在估计平均分布的极值指数。由于异质性,渐近方差可以大大小于i.i.d情况。作为一种特殊情况,我们考虑一个异质尺度模型,其中渐近方差可以显式计算。证明的主要工具是加权尾经验过程的泛函中心极限定理。我们也给出了极值分位数估计的渐近正态性结果。仿真研究表明,我们的极限定理具有良好的有限样本性质。我们也提出应用来评估地震能量的尾重和横截面股市损失。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Extreme value inference for heterogeneous power law data
We extend extreme value statistics to independent data with possibly very different distributions. In particular, we present novel asymptotic normality results for the Hill estimator, which now estimates the extreme value index of the average distribution. Due to the heterogeneity, the asymptotic variance can be substantially smaller than that in the i.i.d. case. As a special case, we consider a heterogeneous scales model where the asymptotic variance can be calculated explicitly. The primary tool for the proofs is the functional central limit theorem for a weighted tail empirical process. We also present asymptotic normality results for the extreme quantile estimator. A simulation study shows the good finite-sample behavior of our limit theorems. We also present applications to assess the tail heaviness of earthquake energies and of cross-sectional stock market losses.
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来源期刊
Annals of Statistics
Annals of Statistics 数学-统计学与概率论
CiteScore
9.30
自引率
8.90%
发文量
119
审稿时长
6-12 weeks
期刊介绍: The Annals of Statistics aim to publish research papers of highest quality reflecting the many facets of contemporary statistics. Primary emphasis is placed on importance and originality, not on formalism. The journal aims to cover all areas of statistics, especially mathematical statistics and applied & interdisciplinary statistics. Of course many of the best papers will touch on more than one of these general areas, because the discipline of statistics has deep roots in mathematics, and in substantive scientific fields.
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