Multivariate statistical theory based on robust statistics

基于稳健统计的多元统计理论

• 批准号: 13640130
• 负责人: SHIRAISHI Taka-aki
• 金额: $ 1.41万
• 依托单位: Yokohama City University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640130/
• 关键词: robust statistics; asymptotic theory; computational simulation; statistical analysis; algorithm; contidence intervals

Statistical estimation procedures are proposed based on studentized robust statistics for location parameters in two-way layouts with interaction. Large sample properties of their procedures as the cell size tends to infinity are investigated. Although Fisher's consistency is assumed in the theory of M-estimators, it is not needed in this paper. By simulation studies, it can be seen that the proposed estimators are more efficient than least squares estimators except for the case where the underlying distribution is normal.Asymptotic confidence intervals of location parameters are proposed in one-and two-sample models. These are robust procedures based on scale-invariant M-statistics. The one-sample procedures have the same robustness as Huber's M-estimators. The asymptotic efficiency of the proposed confidence intervals is given by a numerical integration.In my book entitled "Tokei Kagaku", parametorics, nonparametorics and semiparametorics are discussed. The way of making a selection from the three procedures is stated based on the search of the undelying distribution and goodness of fit tests.

基于具有交互作用的双向布局中位置参数的学生化稳健统计，提出了统计估计程序。研究了当细胞尺寸趋于无穷大时其程序的大样本特性。虽然 M 估计量理论中假设了 Fisher 一致性，但本文不需要这样做。通过仿真研究可以看出，除了基础分布为正态分布的情况外，所提出的估计器比最小二乘估计器更有效。在一样本和二样本模型中提出了位置参数的渐近置信区间。这些是基于尺度不变 M 统计的稳健过程。单样本程序具有与 Huber 的 M 估计器相同的稳健性。所提出的置信区间的渐近效率是通过数值积分给出的。在我题为“Tokei Kagaku”的书中，讨论了参数学、非参数学和半参数学。基于对潜在分布的搜索和拟合优度检验，阐述了从三个过程中进行选择的方法。

项目成果

T.Shiraishi: "Robust estimates of location parameters in two-way layouts with interaction"Journal of Japanese Society of Computational Statistics. 14巻1号. 1-9 (2001)

T. Shiraishi：“双向布局中位置参数的鲁棒估计”，日本计算统计学会杂志，第 14 卷，第 1. 1-9 期（2001 年）。

白石高章: "統計科学・・・パラメトリック、ノンパラメトリック、セミパラメトリック"日本評論社. 300 (2003)

Takaaki Shiraishi：“统计科学...参数、非参数、半参数”Nippon Hyoronsha 300 (2003)。

Shiraishi, T.: "Asymptotic confidence intervals based on M-procedures in one-and two-sample models"J.Japan Statist.Soc.. 34. (2004)

Shiraishi, T.：“基于一样本和二样本模型中的 M 过程的渐近置信区间”J.Japan Statist.Soc.. 34. (2004)

Shiraishi, T.: "Asymptotic confidence intervals based on M-procedures in one - and two - sample models"J.Japan Statistical Soc.. 34・1. (2004)

Shiraishi, T.：“基于一个和两个样本模型中的 M 过程的渐近置信区间”J.Japan Statistical Soc.. 34・1。

Konno, Y.: "Inadmissiblity of the maximum likelihood estimator of normal covariance matrices with the lattice conditional independence"J.Multivariate Anal.. 79. 33-51 (2001)

Konno, Y.：“具有格条件独立性的正态协方差矩阵的最大似然估计量的不可接受性”J.Multivariate Anal.. 79. 33-51 (2001)