Estimation of the Adjusted Standard‐deviatile for Extreme Risks

IF 1 4区 数学 Q3 STATISTICS & PROBABILITY
Haoyu Chen, Tiantian Mao, Fan Yang
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引用次数: 0

Abstract

Abstract In this paper, we modify the Bayes risk for the expectile, the so‐called variantile risk measure, to better capture extreme risks. The modified risk measure is called the adjusted standard‐deviatile. First, we derive the asymptotic expansions of the adjusted standard‐deviatile. Next, based on the first‐order asymptotic expansion, we propose two efficient estimation methods for the adjusted standard‐deviatile at intermediate and extreme levels. By using techniques from extreme value theory, the asymptotic normality is proved for both estimators for independent and identically distributed observations and for ‐mixing time series, respectively. Simulations and real data applications are conducted to examine the performance of the proposed estimators.
极端风险的调整标准差估计
在本文中,我们修改了期望值的贝叶斯风险,即所谓的可变风险度量,以更好地捕捉极端风险。修正后的风险度量称为调整标准差。首先,我们导出了调整标准差的渐近展开式。其次,基于一阶渐近展开式,我们提出了两种有效的中间和极端水平调整标准差估计方法。通过使用极值理论的技术,分别证明了独立和同分布观测值和混合时间序列的估计量的渐近正态性。通过仿真和实际数据应用来检验所提出的估计器的性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Scandinavian Journal of Statistics
Scandinavian Journal of Statistics 数学-统计学与概率论
CiteScore
1.80
自引率
0.00%
发文量
61
审稿时长
6-12 weeks
期刊介绍: The Scandinavian Journal of Statistics is internationally recognised as one of the leading statistical journals in the world. It was founded in 1974 by four Scandinavian statistical societies. Today more than eighty per cent of the manuscripts are submitted from outside Scandinavia. It is an international journal devoted to reporting significant and innovative original contributions to statistical methodology, both theory and applications. The journal specializes in statistical modelling showing particular appreciation of the underlying substantive research problems. The emergence of specialized methods for analysing longitudinal and spatial data is just one example of an area of important methodological development in which the Scandinavian Journal of Statistics has a particular niche.
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