{"title":"巴特利特-南达-皮莱检验统计量的拉普拉斯展开及其误差范围","authors":"H. Wakaki, V. V. Ulyanov","doi":"10.1137/s0040585x97t991635","DOIUrl":null,"url":null,"abstract":"Theory of Probability &Its Applications, Volume 68, Issue 4, Page 570-581, February 2024. <br/> We construct asymptotic expansions for the distribution function of the Bartlett--Nanda--Pillai statistic under the condition that the null linear hypothesis is valid in a multivariate linear model. Computable estimates of the accuracy of approximation are obtained via the Laplace approximation method, which is generalized to integrals for matrix-valued functions.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Laplace Expansion for Bartlett--Nanda--Pillai Test Statistic and Its Error Bound\",\"authors\":\"H. Wakaki, V. V. Ulyanov\",\"doi\":\"10.1137/s0040585x97t991635\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Theory of Probability &Its Applications, Volume 68, Issue 4, Page 570-581, February 2024. <br/> We construct asymptotic expansions for the distribution function of the Bartlett--Nanda--Pillai statistic under the condition that the null linear hypothesis is valid in a multivariate linear model. Computable estimates of the accuracy of approximation are obtained via the Laplace approximation method, which is generalized to integrals for matrix-valued functions.\",\"PeriodicalId\":51193,\"journal\":{\"name\":\"Theory of Probability and its Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-02-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theory of Probability and its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/s0040585x97t991635\",\"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":"Theory of Probability and its Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/s0040585x97t991635","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
摘要
概率论及其应用》（Theory of Probability &Its Applications），第 68 卷第 4 期，第 570-581 页，2024 年 2 月。 在多元线性模型中零线性假设成立的条件下，我们构建了巴特利特-南达-皮莱统计量分布函数的渐近展开式。通过拉普拉斯近似法获得了近似精度的可计算估计值，并将其推广到矩阵值函数的积分。
Laplace Expansion for Bartlett--Nanda--Pillai Test Statistic and Its Error Bound
Theory of Probability &Its Applications, Volume 68, Issue 4, Page 570-581, February 2024. We construct asymptotic expansions for the distribution function of the Bartlett--Nanda--Pillai statistic under the condition that the null linear hypothesis is valid in a multivariate linear model. Computable estimates of the accuracy of approximation are obtained via the Laplace approximation method, which is generalized to integrals for matrix-valued functions.
期刊介绍：
Theory of Probability and Its Applications (TVP) accepts original articles and communications on the theory of probability, general problems of mathematical statistics, and applications of the theory of probability to natural science and technology. Articles of the latter type will be accepted only if the mathematical methods applied are essentially new.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
