{"title":"二元模型中阶限位置和尺度参数的成分等变估计:一个统一的研究","authors":"Naresh Garg, N. Misra","doi":"10.1214/23-bjps562","DOIUrl":null,"url":null,"abstract":"The problem of estimating location (scale) parameters $\\theta_1$ and $\\theta_2$ of two distributions when the ordering between them is known apriori (say, $\\theta_1\\leq \\theta_2$) has been extensively studied in the literature. Many of these studies are centered around deriving estimators that dominate the best location (scale) equivariant estimators, for the unrestricted case, by exploiting the prior information that $\\theta_1 \\leq \\theta_2$. Several of these studies consider specific distributions such that the associated random variables are statistically independent. This paper considers a general bivariate model and general loss function and unifies various results proved in the literature. We also consider applications of these results to a bivariate normal and a Cheriyan and Ramabhadran's bivariate gamma model. A simulation study is also considered to compare the risk performances of various estimators under bivariate normal and Cheriyan and Ramabhadran's bivariate gamma models.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Componentwise equivariant estimation of order restricted location and scale parameters in bivariate models: A unified study\",\"authors\":\"Naresh Garg, N. Misra\",\"doi\":\"10.1214/23-bjps562\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The problem of estimating location (scale) parameters $\\\\theta_1$ and $\\\\theta_2$ of two distributions when the ordering between them is known apriori (say, $\\\\theta_1\\\\leq \\\\theta_2$) has been extensively studied in the literature. Many of these studies are centered around deriving estimators that dominate the best location (scale) equivariant estimators, for the unrestricted case, by exploiting the prior information that $\\\\theta_1 \\\\leq \\\\theta_2$. Several of these studies consider specific distributions such that the associated random variables are statistically independent. This paper considers a general bivariate model and general loss function and unifies various results proved in the literature. We also consider applications of these results to a bivariate normal and a Cheriyan and Ramabhadran's bivariate gamma model. A simulation study is also considered to compare the risk performances of various estimators under bivariate normal and Cheriyan and Ramabhadran's bivariate gamma models.\",\"PeriodicalId\":51242,\"journal\":{\"name\":\"Brazilian Journal of Probability and Statistics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2021-09-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Brazilian Journal of Probability and Statistics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1214/23-bjps562\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Brazilian Journal of Probability and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/23-bjps562","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Componentwise equivariant estimation of order restricted location and scale parameters in bivariate models: A unified study
The problem of estimating location (scale) parameters $\theta_1$ and $\theta_2$ of two distributions when the ordering between them is known apriori (say, $\theta_1\leq \theta_2$) has been extensively studied in the literature. Many of these studies are centered around deriving estimators that dominate the best location (scale) equivariant estimators, for the unrestricted case, by exploiting the prior information that $\theta_1 \leq \theta_2$. Several of these studies consider specific distributions such that the associated random variables are statistically independent. This paper considers a general bivariate model and general loss function and unifies various results proved in the literature. We also consider applications of these results to a bivariate normal and a Cheriyan and Ramabhadran's bivariate gamma model. A simulation study is also considered to compare the risk performances of various estimators under bivariate normal and Cheriyan and Ramabhadran's bivariate gamma models.
期刊介绍:
The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes.
More specifically, the following types of contributions will be considered:
(i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects.
(ii) Original articles developing theoretical results.
(iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it.
(iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.