Mathematical Sciences: Research in Multivariate StatisticalAnalysis

多变量数据分析中的一个中心问题是因素的数量，通常用协方差矩阵的“真实”排名表示。可以对样本协方差矩阵应用各种最优标准；事实上，这些标准是许多标准多变量推断程序的基础，包括主成分分析、因子分析、多变量方差分析和判别程序。这项研究将考察各种模型选择方法，特别注意稳健性。将使用投影寻踪中的思想来得出判别分析的新方法。研究人员在分析对多个变量的观察时，同时面临着确定有多少因素真正重要的问题。在数据中存在正态变化的情况下，用于评估重要因素e个数的统计程序需要保持稳定。这项研究的重点是确定这些因素的数量的可取的新方法，以及当只有适度数量的个人同时观察到许多变量时，确定数据中有趣特征的方法。

A central question in multivariate data analysis is the number of factors, usually couched in terms of the "true" rank of the covariance matrix. A variety of optimality criteria can be applied to the sample covariance matrix; and these are in fact the basis for many standard multivariate inferential procedures including principal components analysis, factor analysis, multivariate analysis of variance and discriminant procedures. This research will examine various model selection methods, giving special attention to robustness. New approaches to discriminant analysis will be drawn using ideas from projection pursuit. Researchers analyzing observations on many variables simul- taneously face the problem of deciding how many factors are really important. The statistical procedures used to assess the e number of important factors needs to be stable in the presence of normal variation present in the data. This research focusses on desirable new methods to determine the number of such factors and also on methodology to identify interesting features in the data when many variables are observed at the same time for only a moderate number of individuals.