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

本研究包括模型中的统计推断，其中多元观察被视为“系统部分”和随机“误差”的总和。系统部分在多元方差模型中是随机的，在因子分析模型中可能是随机的、非随机的或混合的，在许多情况下，它被限制在比观测和误差低维的线性空间中。误差的协方差矩阵可能具有许多特殊的性质；例如，在因子分析中，它是对角线。这项研究属于统计学的一般范畴。所研究的模型在心理测量学和计量经济学中有广泛的应用。在研究中，大样本理论将用于检验关于线性限制数量的假设和确定线性限制数量的程序，以及限制和协方差矩阵的估计。

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.