Distribution problem of discriminant and regression analysis for directional data

方向数据判别回归分析的分布问题

• 批准号: 63530009
• 负责人: HAYAKAWA Takesi
• 金额: $ 1.22万
• 依托单位: HITOTSUBASHI UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1988
• 资助国家: 日本
• 起止时间: 1988 至 1989
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-63530009/
• 关键词: Langevin population; Likelihood ratio criterion; Wald statistic; Watson statistic; Discriminant analysis; Misclassification; Plug-in statistic; Rao statistic; Langerin分布; Wald統計量; Plug-In統計量; Rao統計量; 誤判別確率; 検出力; Langevin分布; 改良Wald統計量; Elli

This research studied the following problems. (1) Tests of parameters (mean direction and concentration parameter) of Langevin population on a sphere. Test statistics (Likelihood ratio criterion, Watson statistic, Wald statistic, Rao statistic etc.) are proposed and asymptotic expansions of the distributions of these are obtained. The simulation experiments show that the asymptotic expansions give good agreements with simulation results. (2) The discriminant functions (Plug-In statistic and Likelihood ratio criterion) for two Langevin populations are proposed. The comparison of these in done from theoretical and simulational points of view. (3) The survey was done for the recent development of zonal polynomials and invariant polynomials which are fundamental ones for the study, of the distributional problems in multivariate analysis.

本研究研究了以下问题。 (1)球体上Langevin布居参数(平均方向和浓度参数)的检验。提出了检验统计量（似然比准则、Watson 统计量、Wald 统计量、Rao 统计量等），并获得了这些分布的渐近展开。仿真实验表明渐近展开式与仿真结果吻合良好。 (2)提出了两个Langevin总体的判别函数（插件统计量和似然比准则）。这些比较是从理论和模拟的角度进行的。 (3)调查了作为研究多元分析中的分布问题的基本多项式的区域多项式和不变多项式的最新发展。

项目成果

T.Hayakawa: "On the tests for the mean direction of the langevin distribution" Ann.Inst.Statist.Math.

T.Hayakawa：“关于朗之万分布平均方向的检验”Ann.Inst.Statist.Math。

T.Hayakawa: "On the distributions of the functions of the F-matrix under an elliptical population" Pour.Statist.Plann.and Inf.21. 41-52 (1989)

T.Hayakawa：“关于椭圆总体下 F 矩阵函数的分布”Pour.Statist.Plann.and Inf.21。

T.Hayakawa: "Discriminant analysis for langevin population"

T.Hayakawa：“朗之万群体的判别分析”

T.Hayakawa: "Invariant polynomials and related tests" Amerrican Jour.Math.and Management Sciences.

T.Hayakawa：“不变多项式和相关测试”美国杂志、数学和管理科学。

T.Hayakawa: Jour.Statist.Plann.and Inf.21. 41-52 (1989)

T.Hayakawa：Jour.Statist.Plann.and Inf.21。