Additive regression splines with total variation and non negative garrote penalties

作     者：Jhong, Jae-Hwan Bak, Kwan-Young Shin, Jae-Kyung Koo, Ja-Yong 

作者机构：Korea Univ Dept Stat Seoul South Korea Chungbuk Natl Univ Dept Informat Stat Cheongju South Korea 

出 版 物：《COMMUNICATIONS IN STATISTICS-THEORY AND METHODS》 (统计学通讯：理论与方法)

年 卷 期：2022年第51卷第22期

页      面：7713-7736页

核心收录：

学科分类：0202[经济学-应用经济学] 02[经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 

基　　金：Basic Science Research Program through the National Research Foundation of Korea (NRF) - Ministry of Education, Science and Technology [NRF-2018R1D1A1B07049972] Korea University Grant NRF [NRF-2020R1G1A1A01100869] 

主　　题：Coordinate descent algorithm model selection non parametric smoothing oracle inequality penalized least squares 

摘      要：This study examines a penalized additive regression spline estimator with total variation and non negative garrote-type penalties. The proposed estimator is obtained based on a two-stage procedure. In the first stage, an initial estimator is obtained via total variation penalization. The total variation penalty enables data-adaptive knot selection and regularizes the overall smoothness of the estimator. The second stage imposes the non negative garrote penalty on the estimated functional components to attain variable selectivity. Regarding the theoretical aspect, a non asymptotic oracle inequality for the total variation penalized estimator is established under some regularity conditions. Based on the oracle inequality, we prove that the estimator attains the optimal rate of convergence up to a logarithmic factor, which in turn leads to the selection and estimation consistency of the second-stage garrote estimator. Numerical studies are presented to illustrate the usefulness of a combination of these two penalties. The results show that the proposed method outperforms existing methods.