Abstract

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.

摘要

这项研究检查了一个惩罚加性回归样条估计器，它具有总变异和非负绞索型惩罚。所提出的估计量是基于两阶段程序获得的。在第一阶段，通过总变差惩罚获得初始估计量。总变异惩罚支持数据自适应节点选择并规范估计器的整体平滑度。第二阶段对估计的功能组件施加非负绞索惩罚，以实现可变选择性。在理论方面，在一定的正则性条件下，建立了全变差惩罚估计量的非渐近预言不等式。基于预言不等式，我们证明了估计器在对数因子下达到了最优收敛速度，这反过来又导致了第二阶段 garrote 估计器的选择和估计一致性。提出了数值研究来说明这两种惩罚组合的有用性。结果表明，所提出的方法优于现有方法。