Abstract
ABSTRACTIn 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|βa| and an optimal bound on .
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