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

作者：Cui, Wenquan^*; Cheng, Haoyang; Sun, Jiajing

来源：Journal of Multivariate Analysis, 2018, 168: 201-210.

DOI：10.1016/j.jmva.2018.07.013

• 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

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 penalty is used to deal with the problem. The estimate of the nonparametric component is subject to a roughness penalty based on the squared semi-norm on the RKHS, and a penalty with oracle properties is used to achieve sparsity in the parametric component. Under regularity conditions, we establish the consistency and rate of convergence of the parametric estimation together with the consistency of variable selection. The proposed estimators of the non-zero coefficients are also shown to have the asymptotic oracle property. Simulations and empirical studies illustrate the performance of the method.

• 出版日期2018-11
• 单位中国科学院大学; 中国科学技术大学