Conditional distance correlation screening for sparse ultrahigh-dimensional models |
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Institution: | 1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China;2. School of Mathematics and Statistics, Wuhan University, Wuhan 430070, China;1. Dpto. Matemática Aplicada, Universidad Politécnica de Madrid (UPM), Avda. Complutense s/n, 28040 Madrid, Spain;2. Dpto. Producción Agraria. E.T.S.I.A.A.B., UPM, 28040 Madrid, Spain;3. CEIGRAM, UPM, Avda. Complutense s/n, 28040 Madrid, Spain;4. Grupo de Sistemas Complejos, E.T.S.I.A.A.B., UPM, 28040 Madrid, Spain |
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Abstract: | This paper is concerned with feature screening for ultrahigh-dimensional covariates under general varying-coefficient models. With the sparsity principle and based on the conditional distance correlation, we develop a new marginal feature screening procedure called CDC-SIS to select significant covariates and show that it possesses the sure screening property and ranking consistency property under some regularity conditions. The proposed procedure enjoys two appealing merits. First, the model we considered is more flexible than traditional varying-coefficients regression models, so the method can be used in a wider range of applications. Second, CDC-SIS can be used directly to deal with grouped predictor variables and multivariate responses. We assess the finite sample properties of the proposed procedure by Monte Carlo studies, and illustrate our method by an empirical analysis of a real data set. Compared with other similar works, our procedure yields better performance. |
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