Constructing theoretical system for high-dimension, low-sample-size data

提出了高维低样本数据的统计理论和方法。我们发现，HDLSS数据有两个不同的几何表示。提出了基于几何表示的降噪方法。本文提出了扩展的交叉数据矩阵方法，它为高维数据分析中出现的参数提供了一个具有小的渐近方差和低计算成本的无偏估计。我们提供了两个有效的判别程序：基于距离的分类器和几何分类器，它可以确保高精度的错误分类率，并保持错误分类率小于一个阈值。

We proposed statistical theories and methodologies for high-dimension, low-sample-size (HDLSS) data. We showed that HDLSS data have two distinct geometric representations. We proposed the noise-reduction methodology that was brought from the geometric representations. We proposed the extended Cross-data-matrix methodology, which offers an unbiased estimator having small asymptotic variance and low computational cost, for parameters appearing in high-dimensional data analysis. We provided two effective discriminant procedures: a distance-based classifier and a geometric classifier, which can ensure high accuracy in misclassification rates and hold misclassification rates less than a threshold.