一般风险泛函的拟hadamard可微性及其应用

IF 1.3 Q2 STATISTICS & PROBABILITY

Statistics & Risk Modeling Pub Date : 2014-01-14 DOI:10.1515/strm-2014-1174

Volker Krätschmer, A. Schied, Henryk Zähle

{"title":"一般风险泛函的拟hadamard可微性及其应用","authors":"Volker Krätschmer, A. Schied, Henryk Zähle","doi":"10.1515/strm-2014-1174","DOIUrl":null,"url":null,"abstract":"Abstract We apply a suitable modification of the functional delta method to statistical functionals that arise from law-invariant coherent risk measures. To this end we establish differentiability of the statistical functional in a relaxed Hadamard sense, namely with respect to a suitably chosen norm and in the directions of a specifically chosen “tangent space”. We show that this notion of quasi-Hadamard differentiability yields both strong laws and limit theorems for the asymptotic distribution of the plug-in estimators. Our results can be regarded as a contribution to the statistics and numerics of risk measurement and as a case study for possible refinements of the functional delta method through fine-tuning the underlying notion of differentiability.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2014-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/strm-2014-1174","citationCount":"17","resultStr":"{\"title\":\"Quasi-Hadamard differentiability of general risk functionals and its application\",\"authors\":\"Volker Krätschmer, A. Schied, Henryk Zähle\",\"doi\":\"10.1515/strm-2014-1174\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We apply a suitable modification of the functional delta method to statistical functionals that arise from law-invariant coherent risk measures. To this end we establish differentiability of the statistical functional in a relaxed Hadamard sense, namely with respect to a suitably chosen norm and in the directions of a specifically chosen “tangent space”. We show that this notion of quasi-Hadamard differentiability yields both strong laws and limit theorems for the asymptotic distribution of the plug-in estimators. Our results can be regarded as a contribution to the statistics and numerics of risk measurement and as a case study for possible refinements of the functional delta method through fine-tuning the underlying notion of differentiability.\",\"PeriodicalId\":44159,\"journal\":{\"name\":\"Statistics & Risk Modeling\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2014-01-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1515/strm-2014-1174\",\"citationCount\":\"17\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Statistics & Risk Modeling\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/strm-2014-1174\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistics & Risk Modeling","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/strm-2014-1174","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

引用次数: 17

摘要

摘要:我们应用了一种适当的修正的泛函增量方法来处理由规律不变的相干风险度量产生的统计泛函。为此，我们在松弛的Hadamard意义上建立统计泛函的可微性，即关于适当选择的范数和在特定选择的“切空间”方向上的可微性。我们证明了这个拟hadamard可微性的概念给出了插件估计量渐近分布的强定律和极限定理。我们的结果可以被视为对风险测量的统计和数值的贡献，并作为通过微调可微性的基本概念来改进函数增量方法的案例研究。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Quasi-Hadamard differentiability of general risk functionals and its application

Abstract We apply a suitable modification of the functional delta method to statistical functionals that arise from law-invariant coherent risk measures. To this end we establish differentiability of the statistical functional in a relaxed Hadamard sense, namely with respect to a suitably chosen norm and in the directions of a specifically chosen “tangent space”. We show that this notion of quasi-Hadamard differentiability yields both strong laws and limit theorems for the asymptotic distribution of the plug-in estimators. Our results can be regarded as a contribution to the statistics and numerics of risk measurement and as a case study for possible refinements of the functional delta method through fine-tuning the underlying notion of differentiability.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Statistics & Risk Modeling STATISTICS & PROBABILITY-

CiteScore

1.80

自引率

6.70%

发文量

期刊介绍： Statistics & Risk Modeling (STRM) aims at covering modern methods of statistics and probabilistic modeling, and their applications to risk management in finance, insurance and related areas. The journal also welcomes articles related to nonparametric statistical methods and stochastic processes. Papers on innovative applications of statistical modeling and inference in risk management are also encouraged. Topics Statistical analysis for models in finance and insurance Credit-, market- and operational risk models Models for systemic risk Risk management Nonparametric statistical inference Statistical analysis of stochastic processes Stochastics in finance and insurance Decision making under uncertainty.