The partial linear model in high dimensions

TL;DR

This paper investigates high-dimensional partial linear models, demonstrating that the linear component can be efficiently estimated using LASSO and smoothness penalties, achieving oracle rates.

Contribution

It introduces a method combining LASSO and smoothness penalties for high-dimensional partial linear models, achieving optimal estimation rates.

Findings

Linear part estimated at oracle rates

LASSO penalty effectively handles high-dimensionality

Method applicable to models with non-parametric components

Abstract

Partial linear models have been widely used as flexible method for modelling linear components in conjunction with non-parametric ones. Despite the presence of the non-parametric part, the linear, parametric part can under certain conditions be estimated with parametric rate. In this paper, we consider a high-dimensional linear part. We show that it can be estimated with oracle rates, using the LASSO penalty for the linear part and a smoothness penalty for the nonparametric part.