Variable selection of linear programming discriminant estimator. Issue 7 (3rd April 2017)

• Record Type: Journal Article
• Authors: Xia, Dong
• Is Part Of: Communications in statistics. Volume 46:Issue 7(2017)
• Page Start: 3321
• Page End: 3341
• Publication Date: 2017-04-03
• Subjects: Linear classification -- sparsity -- sign consistency -- irrepresentable condition; Primary 62H30 -- Secondary 62F12; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2015.1060344
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: In this paper, the variable selection property will be studied for the linear programming discriminant (LPD) estimator, denoted by with n being the sample size. The LPD estimator is used in high-dimensional linear discriminant analysis under the assumption that the Bayes direction is sparse which has support T . More exactly, we will study the property as n → ∞, which means sign consistency. A sufficient condition will be proposed under which the sign consistency property holds as log ( p ) ⩽ cn for small enough c > 0. The result is also non asymptotic. Our result gives optimal bounds on n and min a ∈ T |β a | and an optimal bound on .