New developments of theories in multivariate statistical inference and their applications

本课题在多元统计模型的估计、假设检验、预测和变量选择等方面提出了新的方法，并提出了新方法的合理性理论。特别是，我们处理的问题，模型或情况下，传统的方法有缺陷的使用或不可用，然后我们试图推导和建议的程序，可以解决问题。其中，解决了以下多变量统计问题，并开发了新的理论和应用：（1）小区域估计中均方误差和置信区间的高阶渐近校正，（2）连续和离散混合模型下小区域估计中的基准问题，（3）线性混合模型中Bartlett校正和变量选择方法，（4）线性判别的高维过程;（5）多维参数估计的最优性。

In this research project, new procedures were derived in estimation, hypothesis testing, predction and variable selection in multivariate statistical models as well as theories for justfying the new procedures were developed. In particular, we treated problems, models or situations where conventional methods had drawbacks for use or were not available, and then we tried to derive and suggest procedures which could resolve the problems. Of these, the following multivatiate statistical issues were addressed and new theories were developed with applications: (1) higher order asymptotic corrections in mean squared errors and confidence intervals in small area estimation, (2) benchmark problems in small area estimation under continuous and discrete mixed models, (3) Bartlett corrections and methods for variable selection in linear mixed models, (4) high dimensional procedures in linear discrimination and (5) optimality in estimation of multi-dimensional parameters.