An RKHS-based approach to double-penalized regression in high-dimensional partially linear models

• Published in: Journal of multivariate analysis Vol. 168; pp. 201 - 210
• Main Authors: Cui, Wenquan, Cheng, Haoyang, Sun, Jiajing
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.11.2018
• Subjects: Eigen-analysis; High-dimensional data; Oracle property; Partially linear model; Representer theorem; Reproducing kernel Hilbert space; Sacks–Ylvisaker conditions; SCAD (smoothly clipped absolute deviation) penalty; High-dimensional data; Eigen-analysis; Reproducing kernel Hilbert space; 62G08; Sacks–Ylvisaker conditions; 62J07; Oracle property; 62G20; Representer theorem; 62F12; Partially linear model; SCAD (smoothly clipped absolute deviation) penalty

We study simultaneous variable selection and estimation in high-dimensional partially linear models under the assumption that the nonparametric component is from a reproducing kernel Hilbert space (RKHS) and that the vector of regression coefficients for the parametric component is sparse. A double...