{"title":"Rates of convergence of powered order statistics from general error distribution","authors":"Yuhan Zou, Yingyin Lu, Zuoxiang Peng","doi":"10.1080/24754269.2022.2146955","DOIUrl":null,"url":null,"abstract":"Let be a sequence of independent random variables with common general error distribution with shape parameter v>0, and let denote the r-th largest order statistics of . With different normalizing constants the distributional expansions and the uniform convergence rates of normalized powered order statistics are established. An alternative method is presented to estimate the probability of the r-th extremes. Numerical analyses are provided to support the main results.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"7 1","pages":"1 - 29"},"PeriodicalIF":0.7000,"publicationDate":"2022-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistical Theory and Related Fields","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1080/24754269.2022.2146955","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 1
Abstract
Let be a sequence of independent random variables with common general error distribution with shape parameter v>0, and let denote the r-th largest order statistics of . With different normalizing constants the distributional expansions and the uniform convergence rates of normalized powered order statistics are established. An alternative method is presented to estimate the probability of the r-th extremes. Numerical analyses are provided to support the main results.
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