Linear and Quadratic Discriminant Analyses for High-Dimensional Data

• Activity Number: 53
• Type: Invited
• Date/Time: Sunday, August 9, 2015 : 4:00 PM to 5:50 PM
• Sponsor: SSC
• Author(s): Yingli Qin* and Yilei Wu and Mu Zhu
• Companies: University of Waterloo and University of Waterloo and University of Waterloo
• Keywords: classification ; Fisher's rule ; linear discriminant analysis ; population eigenvalue ; quadratic discriminant analysis

Abstract

High-dimensional classification is an important and challenging statistical problem. We consider both linear and quadratic discriminant rules which do not require sparsity assumptions --- either on the covariance matrices of each class (or their inverses), or on the standardized between-class distance. Under moderate conditions on the eigenvalues of population covariance matrices, our 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 also present real-data analyses of several classical micro-array data sets.