Statistical Inference under the Strongly Spiked Eigenvalue Model

Abstract

In this paper, we introduce high-dimensional statistical analysis for the Strongly Spiked Eigenvalue (SSE) model. We deal with statistical inference for non-sparse high-dimensional data, such as genomic data, especially equality test of high-dimensional covariance matrices and quadratic discriminant analysis. In statistical inference, the key to guaranteeing theoretical accuracy is the high-dimensional asymptotic normality of the statistic. However, high-dimensional asymptotic normality does not generally hold for high-dimensional data belonging to the SSE model. New techniques are needed to derive asymptotic distributions of statistics and to handle the data instead of high-dimensional asymptotic normality. We describe ideas on how to approach the SSE model and guarantee high accuracy, as well as the latest developments in high-dimensional statistical analysis.