Variable selection for partially linear models via learning gradients

Document Type

Article

Publication Date

1-1-2017

Abstract

Partially linear models (PLMs) are important generalizations of linear models and are very useful for analyzing high-dimensional data. Compared to linear models, the PLMs possess desirable flexibility of nonparametric regression models because they have both linear and non-linear components. Variable selection for PLMs plays an important role in practical applications and has been extensively studied with respect to the linear component. However, for the non-linear component, variable selection has been well developed only for PLMs with extra structural assumptions such as additive PLMs and generalized additive PLMs. There is currently an unmet need for variable selection methods applicable to general PLMs without structural assumptions on the non-linear component. In this paper, we propose a new variable selection method based on learning gradients for general PLMs without any assumption on the structure of the non-linear component. The proposed method utilizes the reproducing-kernel-Hilbert-space tool to learn the gradients and the group-lasso penalty to select variables. In addition, a block-coordinate descent algorithm is suggested and some theoretical properties are established including selection consistency and estimation consistency. The performance of the proposed method is further evaluated via simulation studies and illustrated using real data.

Identifier

85027417141 (Scopus)

Publication Title

Electronic Journal of Statistics

External Full Text Location

https://doi.org/10.1214/17-EJS1300

ISSN

19357524

First Page

2907

Last Page

2930

Issue

2

Volume

11

Grant

P30 AG008051

Fund Ref

National Institutes of Health

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