A consistent variable selection method in high-dimensional canonical discriminant analysis

Abstract In this paper, we obtain the sufficient conditions to determine the consistency of a variable selection method based on a generalized information criterion in canonical discriminant analysis. To examine the consistency property, we use a high-dimensional asymptotic framework such that as the sample size n goes to infinity, then the ratio of the length of the observation vector p to the sample size, p ∕ n , converges to a constant that is less than one even if the dimension of the observation vector also goes to infinity. Using the derived conditions, we propose a consistent variable selection method. From numerical simulations, we show that the probability of selecting the true model by our proposed method is high even when p is large. Further, the advantage of the proposed method is demonstrated by a real data.