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