New Developments of Multivariate Statistical Methodologies - High Speed, Robustness, and High Accuracy

在这个研究项目中，我们的目标是开发新的多元统计方法，以满足对现代数据进行推断的高速、稳健性和高精度的标准。我们提供了三种多元统计方法，以确保稳健性和高精度，即使对非高斯污染模型也是如此。研究结果如下：(1)发展了基于高阶矩的高速、高精度分类方法。(2)发展高速、高精度的变量选择和离群点检测方法。(3)污染数据空间中的本征空间分析。

In this research project, we aim to develop new multivariate statistical methods satisfying the criteria of high speed, robustness and high accuracy for inferences on modern data. We provided three multivariate statistical methods to ensure robustness and high accuracy with low computational cost even for non-Gaussian, contaminated models. The findings of this research are as follows: (1) Developments of high-speed and highly accurate classification methods using higher moments. (2) Developments of high-speed and highly accurate variable selection and outlier detection methods. (3) Intrinsic space analysis in a contaminated data space.