Mathematical Sciences: Multivariate Components of Variance, Factor Analysis, and Principal Component Analysis

这项研究包括将多变量观测值视为“系统部分”和随机“误差”之和的模型中的统计推断。系统部分在方差模型的多变量分量中是随机的，在因子分析模型中可以是随机的、非随机的或混合的，在许多情况下被限制在比观测值和误差更低的维线性空间中。误差的协方差矩阵可能具有许多特殊性质；例如，在因子分析中，它是对角的。这项研究属于统计学的一般领域。研究中研究的模型广泛应用于心理计量学和计量经济学。在研究中，将发展大样本理论来检验关于线性约束数目的假设和确定线性约束数目的程序，以及用于约束和协方差矩阵的估计量。

This research includes statistical inference in models in which the multivariate observation is treated as the sum of a 'systematic part' and a random 'error'. The systematic part, which is stochastic in the multivariate components of variance model and may be stochastic, nonstochastic, or mixed in the factor analysis models, is in many cases restricted to a linear space of lower dimension than the observation and error. The covariance matrix of the error may have many special properties; for example, in factor analysis it is diagonal. This research is in the general area of statistics. The models studied in the research are used extensively in psychometrics and econometrics. In the research large-sample theory will be developed for tests of hypotheses concerning the number of linear restrictions and procedures to determine the number of linear restrictions, and for the estimators of the restrictions and the covariance matrices.