Statistical hypothesis testing for high-dimension, low-sample-size data

In this editorial, we explain statistical inference for high-dimension, low-sample-size (HDLSS) data in detail. Our target HDLSS data are those characterized by nonsparsity, for example, genome data. The nonsparsity characteristic of HDLSS data makes it extremely difficult to guarantee accuracy in statistical inference because latent information is buried in a huge amount of noise. In order to overcome the difficulty, the authors have developed a new theory of high-dimensional statistical analysis and a new methodology of nonsparse modeling. We explain how to handle the troublesome noise and give theories and methodologies to guarantee high accuracy in statistical inference. We introduce two types of high-dimensional eigenvalue models and the high-dimensional central limit theorem. Two-sample tests for high-dimensional mean vectors and equality tests of high-dimensional covariance matrices are given together with examples of microarray data sets.