康托罗维奇和维兰德不等式的一般化及其在统计学中的应用

IF 2.3 3区数学 Q1 MATHEMATICS

Mathematics Pub Date : 2024-09-14 DOI:10.3390/math12182860

Yunzhi Zhang, Xiaotian Guo, Jianzhong Liu, Xueping Chen

{"title":"康托罗维奇和维兰德不等式的一般化及其在统计学中的应用","authors":"Yunzhi Zhang, Xiaotian Guo, Jianzhong Liu, Xueping Chen","doi":"10.3390/math12182860","DOIUrl":null,"url":null,"abstract":"By utilizing the properties of positive definite matrices, mathematical expectations, and positive linear functionals in matrix space, the Kantorovich inequality and Wielandt inequality for positive definite matrices and random variables are obtained. Some novel Kantorovich type inequalities pertaining to matrix ordinary products, Hadamard products, and mathematical expectations of random variables are provided. Furthermore, several interesting unified and generalized forms of the Wielandt inequality for positive definite matrices are also studied. These derived inequalities are then exploited to establish an inequality regarding various correlation coefficients and study some applications in the relative efficiency of parameter estimation of linear statistical models.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generalizations of the Kantorovich and Wielandt Inequalities with Applications to Statistics\",\"authors\":\"Yunzhi Zhang, Xiaotian Guo, Jianzhong Liu, Xueping Chen\",\"doi\":\"10.3390/math12182860\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"By utilizing the properties of positive definite matrices, mathematical expectations, and positive linear functionals in matrix space, the Kantorovich inequality and Wielandt inequality for positive definite matrices and random variables are obtained. Some novel Kantorovich type inequalities pertaining to matrix ordinary products, Hadamard products, and mathematical expectations of random variables are provided. Furthermore, several interesting unified and generalized forms of the Wielandt inequality for positive definite matrices are also studied. These derived inequalities are then exploited to establish an inequality regarding various correlation coefficients and study some applications in the relative efficiency of parameter estimation of linear statistical models.\",\"PeriodicalId\":18303,\"journal\":{\"name\":\"Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2024-09-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3390/math12182860\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3390/math12182860","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

利用矩阵空间中的正定矩阵、数学期望和正线性函数的性质，得到了正定矩阵和随机变量的康托洛维奇不等式和维兰德不等式。还提供了一些与矩阵常乘积、哈达玛乘积和随机变量的数学期望有关的新颖的 Kantorovich 型不等式。此外，还研究了正定矩阵维兰德不等式的几种有趣的统一和广义形式。然后，利用这些导出的不等式建立了关于各种相关系数的不等式，并研究了线性统计模型参数估计相对效率中的一些应用。

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

Generalizations of the Kantorovich and Wielandt Inequalities with Applications to Statistics

By utilizing the properties of positive definite matrices, mathematical expectations, and positive linear functionals in matrix space, the Kantorovich inequality and Wielandt inequality for positive definite matrices and random variables are obtained. Some novel Kantorovich type inequalities pertaining to matrix ordinary products, Hadamard products, and mathematical expectations of random variables are provided. Furthermore, several interesting unified and generalized forms of the Wielandt inequality for positive definite matrices are also studied. These derived inequalities are then exploited to establish an inequality regarding various correlation coefficients and study some applications in the relative efficiency of parameter estimation of linear statistical models.

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

Mathematics Mathematics-General Mathematics

CiteScore

4.00

自引率

16.70%

发文量

4032

审稿时长

21.9 days

期刊介绍： Mathematics (ISSN 2227-7390) is an international, open access journal which provides an advanced forum for studies related to mathematical sciences. It devotes exclusively to the publication of high-quality reviews, regular research papers and short communications in all areas of pure and applied mathematics. Mathematics also publishes timely and thorough survey articles on current trends, new theoretical techniques, novel ideas and new mathematical tools in different branches of mathematics.