QUADRATIC DISCRIMINANT ANALYSIS FOR HIGH-DIMENSIONAL DATA

摘要

High-dimensional classification is an important and challenging statistical problem. We develop a set of quadratic discriminant rules by simplifying the structure of the covariance matrices instead of imposing sparsity assumptions either on the covariance matrices themselves (or their inverses), or on the standardized between-class distance. Under moderate conditions on the population covariance matrices, our quadratic discriminant rules enjoy good asymptotic properties. Computationally, they are easy to implement and do not require large-scale mathematical programming. Numerically, they perform well in finite dimensions and with finite sample sizes. We present analyses of several classic micro-array data sets.