关于极值理论中密度函数与Rényi熵的收敛速度

IF 0.4 Q4 STATISTICS & PROBABILITY

Theory of Probability and Mathematical Statistics Pub Date : 2023-05-02 DOI:10.1090/tpms/1191

Ali Saeb

{"title":"关于极值理论中密度函数与Rényi熵的收敛速度","authors":"Ali Saeb","doi":"10.1090/tpms/1191","DOIUrl":null,"url":null,"abstract":"De Haan and Resnick [Ann. Probab. 10 (1982), no. 2, 396–413] have shown that the Rényi entropy of order \n\n \n β\n \\beta\n \n\n (\n\n \n \n β\n >\n 1\n \n \\beta >1\n \n\n) of normalized sample maximum of independent and identically distributed (iid) random variables with continuous differentiable density converges to the Rényi entropy of order \n\n \n β\n \\beta\n \n\n of a max stable law. In this paper, we review the rate of convergence for density function in extreme value theory. Finally, we study the rate of convergence for Rényi entropy in the case of normalized sample maxima.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2023-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A comment on rates of convergence for density function in extreme value theory and Rényi entropy\",\"authors\":\"Ali Saeb\",\"doi\":\"10.1090/tpms/1191\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"De Haan and Resnick [Ann. Probab. 10 (1982), no. 2, 396–413] have shown that the Rényi entropy of order \\n\\n \\n β\\n \\\\beta\\n \\n\\n (\\n\\n \\n \\n β\\n >\\n 1\\n \\n \\\\beta >1\\n \\n\\n) of normalized sample maximum of independent and identically distributed (iid) random variables with continuous differentiable density converges to the Rényi entropy of order \\n\\n \\n β\\n \\\\beta\\n \\n\\n of a max stable law. In this paper, we review the rate of convergence for density function in extreme value theory. Finally, we study the rate of convergence for Rényi entropy in the case of normalized sample maxima.\",\"PeriodicalId\":42776,\"journal\":{\"name\":\"Theory of Probability and Mathematical Statistics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-05-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theory of Probability and Mathematical Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/tpms/1191\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Probability and Mathematical Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/tpms/1191","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

引用次数: 1

摘要

De Haan和Resnick[Ann.Probab.10（1982），no.2396–413]已经表明，具有连续可微密度的独立同分布（iid）随机变量的归一化样本极大值的β\β阶Rényi熵（β>1\β>1）收敛于极大稳定律的β\贝塔阶Rény熵。本文讨论了极值理论中密度函数的收敛速度。最后，我们研究了Rényi熵在归一化样本最大值情况下的收敛速度。

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

A comment on rates of convergence for density function in extreme value theory and Rényi entropy

De Haan and Resnick [Ann. Probab. 10 (1982), no. 2, 396–413] have shown that the Rényi entropy of order β \beta ( β > 1 \beta >1 ) of normalized sample maximum of independent and identically distributed (iid) random variables with continuous differentiable density converges to the Rényi entropy of order β \beta of a max stable law. In this paper, we review the rate of convergence for density function in extreme value theory. Finally, we study the rate of convergence for Rényi entropy in the case of normalized sample maxima.

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

Theory of Probability and Mathematical Statistics STATISTICS & PROBABILITY-

CiteScore

1.30

自引率

0.00%

发文量