High-dimensional linear discriminant analysis with moderately clipped LASSO

자연과학 > 통계학
( Jaeho Chang ) , ( Haeseong Moon ) , ( Sunghoon Kwon )
CSAM(Communications for Statistical Applications and Methods) 2021년, 제28권 제1호, 21~37페이지(총17페이지)
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    There is a direct connection between linear discriminant analysis (LDA) and linear regression since the direction vector of the LDA can be obtained by the least square estimation. The connection motivates the penalized LDA when the model is high-dimensional where the number of predictive variables is larger than the sample size. In this paper, we study the penalized LDA for a class of penalties, called the moderately clipped LASSO (MCL), which interpolates between the least absolute shrinkage and selection operator (LASSO) and minimax concave penalty. We prove that the MCL penalized LDA correctly identifies the sparsity of the Bayes direction vector with probability tending to one, which is supported by better finite sample performance than LASSO based on concrete numerical studies.
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