The Partial Linear Model in High Dimensions
By Patrice Müller, Sara A. van de Geer. 2013
47 citations recorded by the source corpus.
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 least absolute shrinkage and selection operator penalty for the linear part and a smoothness penalty for the nonparametric part.
Subfields: Computer Vision and Pattern Recognition, Environmental Engineering, Statistics and Probability
How researchers see this paper
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In Computer Vision and Pattern Recognition
In Environmental Engineering
In Statistics and Probability
- Sara A. van de Geer
- Cun-Hui Zhang
- Peter Buhlmann
- Tong Zhang
- Victor Chernozhukov
- Nicolai Meinshausen
- Alexandre Belloni
- Alexandre B. Tsybakov
Citations in the corpus
- On the uniform convergence of empirical norms and inner products, with application to causal inference (2013, methodology): “Related is the paper [20] where the additive model is studied with f a highdimensional linear function.”