Additive partially linear models for ultra-high-dimensional regression
Date
2019-03-29
Authors
Major Professor
Advisor
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Wiley
Abstract
We consider a semiparametric additive partially linear regression model (APLM) for analyzing ultra-highdimensional data where both the number of linear components and the number of nonlinear components can be much larger than the sample size. We propose a two-step approach for estimation, selection and simultaneous inference of the components in the APLM. In the first step, the nonlinear additive components are approximated using polynomial spline basis functions, and a doubly penalized procedure is
proposed to select nonzero linear and nonlinear components based on adaptive LASSO. In the second step, local linear smoothing is then applied to the data with the selected variables to obtain the asymptotic distribution of the estimators of the nonparametric functions of interest. The proposed method selects the correct model with probability approaching one under regularity conditions. The estimators of both the linear part and nonlinear part are consistent and asymptotically normal, which enables us to construct
confidence intervals and make inferences about the regression coefficients and the component functions. The performance of the method is evaluated by simulation studies. The proposed method is also applied to a dataset on the Shoot Apical Meristem (SAM) of maize genotypes.
Series Number
Journal Issue
Is Version Of
Versions
Series
Academic or Administrative Unit
Type
article
Comments
This is the peer reviewed version of the following article: Li, Xinyi, Li Wang, and Dan Nettleton. "Additive partially linear models for ultra‐high‐dimensional regression." Stat 8, no. 1 (2019): e223, which has been published in final form at doi:https://doi.org/10.1002/sta4.223. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.