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

在本研究项目中，我们的目标是开发新的多元统计方法，满足高速、鲁棒性和高精度的标准，用于现代数据的推断。我们提供了三种多元统计方法，即使对于非高斯污染模型，也能以低计算成本确保鲁棒性和高精度。主要研究成果如下：(1)基于高矩的高速高精度分类方法的发展。(2)高速高精度变量选择和离群值检测方法的发展。(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.