Title: RKHS-based approach to SCAD-penalized regression in high-dimensional partially linear models
Authors: Wenquan Cui - University of Science and Technology of China (Austria)
Haoyang Cheng - University of Science and Technology of China (China)
Jiajing Sun - University of Chinese Academy of Sciences (China) [presenting]
Abstract: The high-dimensional partially linear models relevant for the problem of simultaneous variable selection and estimation, are studied under the assumptions that the function of the nonparametric part is derived from a reproducing kernel Hilbert space (RKHS) and the vector of regression coefficients for parametric component is sparse. A double penalties is provided to deal with the problem, with the roughness penalty of squared semi-norm on RKHS deployed to estimate the nonparametric component and the SCAD penalty used to achieve sparsity in the parametric part. Under some regular conditions, we establish the rate of convergence and consistency of the parametric estimation together with the consistency of variable selection. Furthermore, the presented estimators of the non-zero coefficients are shown to have the asymptotic oracle property. They are asymptotically normal with the same means and covariances that they would have if the zero coefficients were known in advance. Simulations are conducted to demonstrate the performance of the proposed method. Empirical analysis is also included.