Mathematical Sciences: Research in Multivariate Statistical Analysis

多元统计分析的研究将集中在与随机矩阵和参数矩阵的特征结构有关的问题上。主元分析、因子分析、典型相关、多元方差分析和判别分析中涉及嵌套假设的顺序检验的推理问题将被研究。将研究改进测试程序的方法。另一个研究的重点是特征结构的估计，重点是发展多元方差分析、多重判别分析和典型相关分析中的最优、准确和可靠的特征值估计。我们将研究将标准估值缩小到某个中心值的技术。另一个研究主题涉及稳健性，重点是投影寻踪技术在判别分析领域的使用。

Research in multivariate statistical analysis will focus on problems related to the eigenstructure of random and parameter matrices. Inference problems in principal components, factor analysis, canonical correlations, multivariate analysis of variance and discriminant analysis that involve sequential testing of nested hypotheses will be examined. Ways of improving the testing procedures will be studied. Another focus of research is the estimation of the eigenstructures with the emphasis on the development of optimal, accurate and reliable estimates of eigenvalues in multivariate analysis of variance, multiple discriminant analysis and canonical correlation analysis. The technique of shrinking standard estimates towards some central value will be examined. Another topic of research is concerned with robustness and focuses on the use of projection pursuit techniques in the area of discriminant analysis.