-A A +A
In this paper we study sparse high dimensional additive partial linear models with nonparametric additive components of heterogeneous smoothness. We review several existing algorithms that have been developed for this problem in the recent literature, highlighting the connections between them, and present some computationally efficient algorithms for fitting such models. To achieve optimal rates in large sample situations we use hybrid P-splines and block wavelet penalisation techniques combined with adaptive (group) LASSO-like procedures for selecting the additive components in the nonparametric part of the models. Hence, the component selection and estimation in the nonparametric part may be viewed as a functional version of estimation and grouped variable selection. This allows to take advantage of several oracle results which yield asymptotic optimality of estimators in high-dimensional but sparse …
South African Statistical Association (SASA)
Publication date: 
1 Dec 2017

Umberto Amato, Anestis Antoniadis, Italia De Feis, Yannig Goude

Biblio References: 
Volume: 51 Issue: 2 Pages: 235-272
South African Statistical Journal