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Asymptotic expansions of the estimators in covariance structures with some robustness issues on normal-theory asymptotic cumulants under nonnormality

协方差结构中估计量的渐近展开，以及非正态下正态理论渐近累积量的一些鲁棒性问题

基本信息

批准号：
18500210
负责人：
OGASAWARA Haruhiko
金额：
$ 1.45万
依托单位：
Otaru University of Commerce
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2006
资助国家：
日本
起止时间：
2006 至 2007
项目状态：
已结题

项目摘要

(1) Methods of asymptotic expansionEdgeworth expansion and its variations have been employed as basic tools. Since data in practice are more or less nonnormally distributed, arbitrary distributions including the normal one as a special case are assumed for observable variables.(2) Asymptotic expansions for the sample correlation coefficientAsymptotic expansions for the sample correlation coefficient and the sample multiple correlation coefficient are obtained up to order 1/n under nonnormality using the Edgeworth expansion and related methods. Asymptotic robustness of the normal-theory lower-order asymptotic cumulants are also investigated.(3) Asymptotic expansions in factor analysisAsymptotic expansions of the non-Studentized estimators and the Studentized ones in factor analysis are given. For Studentization, the sample cumulants up to the fourth order are required and expected to be unstable in finite samples. Considering this property, the Studentized estimators are given under normality and under nonnormality.(4) Asymptotic expansion for the sample coefficient alphaThe sample coefficient alpha is used as an index of reliability in the behavioral sciences. Reliability indexes are defined for correlation matrices as well as covariance matrices. The expansions of the distributions of the estimators have been derived using the Edgeworth expansion.

(1)渐近扩展方法edgeworth展开及其变体作为基本工具。由于实际数据或多或少是非正态分布，对于可观测变量，假设任意分布，包括作为特殊情况的正态分布。(2)样本相关系数的渐近展开式利用Edgeworth展开式及相关方法，在非正态性下得到了样本相关系数和样本多重相关系数的渐近展开式，展开式可达1/n阶。研究了正态理论低阶渐近累积量的渐近鲁棒性。(3)因子分析中的渐近展开式给出了因子分析中非学生化估计量和学生化估计量的渐近展开式。对于学生化，样本累积量高达四阶是必需的，并且预计在有限样本中是不稳定的。考虑到这一性质，给出了正态和非正态下的学生化估计量。(4)样本系数alpha的渐近展开式样本系数alpha在行为科学中被用作可靠性指标。定义了相关矩阵和协方差矩阵的信度指标。利用Edgeworth展开式导出了估计量分布的展开式。