{"title":"On Minimaxity and Limit of Risks Ratio of James-Stein Estimator Under the Balanced Loss Function","authors":"Abdenour Hamdaoui, A. Benkhaled, M. Terbeche","doi":"10.46793/kgjmat2303.459h","DOIUrl":null,"url":null,"abstract":"The problem of estimating the mean of a multivariate normal distribution by different types of shrinkage estimators is investigated. Under the balanced loss function, we establish the minimaxity of the James-Stein estimator. When the dimension of the parameters space and the sample size tend to infinity, we study the asymptotic behavior of risks ratio of James-Stein estimator to the maximum likelihood estimator. The positive-part of James-Stein estimator is also treated.","PeriodicalId":44902,"journal":{"name":"Kragujevac Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kragujevac Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46793/kgjmat2303.459h","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The problem of estimating the mean of a multivariate normal distribution by different types of shrinkage estimators is investigated. Under the balanced loss function, we establish the minimaxity of the James-Stein estimator. When the dimension of the parameters space and the sample size tend to infinity, we study the asymptotic behavior of risks ratio of James-Stein estimator to the maximum likelihood estimator. The positive-part of James-Stein estimator is also treated.
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