Estimation of the adjusted standard‐deviatile for extreme risks

Author:

Chen Haoyu1,Mao Tiantian1,Yang Fan2ORCID

Affiliation:

1. Department of Statistics and Finance, School of Management, School of Data Science University of Science and Technology of China Hefei China

2. Department of Statistics and Actuarial Science University of Waterloo Waterloo Ontario Canada

Abstract

AbstractIn 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.

Funder

Natural Science Foundation of Anhui Province

National Natural Science Foundation of China

Natural Sciences and Engineering Research Council of Canada

Publisher

Wiley

Subject

Statistics, Probability and Uncertainty,Statistics and Probability

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