Sparse Semiparametric Discriminant Analysis

• Activity Number: 474
• Type: Invited
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: WNAR
• Author(s): Hui Zou*+ and Qing Mai
• Companies: University of Minnesota and Florida State University
• Keywords: Gaussian copulas ; Linear discriminant analysis ; Semiparametric model

Abstract

In recent years, a considerable amount of work has been devoted to generalizing linear discriminant analysis to overcome its incompetence for high-dimensional classification (Witten & Tibshirani 2011, Cai & Liu 2011, Mai et al. 2012, Fan et al. 2012). In this paper, we develop high-dimensional sparse semiparametric discriminant analysis (SSDA) that generalizes the normal-theory discriminant analysis in two ways: it relaxes the Gaussian assumptions and can handle ultra-high dimension classification problems. If the underlying Bayes rule is sparse, SSDA can estimate the Bayes rule and select the true features simultaneously with overwhelming probability, as long as the logarithm of dimension grows slower than the cube root of sample size. Simulated and real examples are used to demonstrate the finite sample performance of SSDA.