Statistical inference for high-dimension, low-sample-size data

In this paper, we consider statistical inference for high-dimension, low-sample-size (HDLSS) data. We first show that HDLSS data have distinct geometric representations depending on whether or not the data meets a certain boundary condition. We clarify the limit of the conventional principal component analysis (PCA) for HDLSS data. In order to overcome the curse of dimensionality, we introduce two effective PCAs called the