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Semiparametric Regression Pursuit
Journal article   Peer reviewed

Semiparametric Regression Pursuit

Jian Huang, Fengrong Wei and Shuangge Ma
Statistica Sinica, Vol.22(4), pp.1403-1426
10/01/2012
DOI: 10.5705/ss.2010.298
PMCID: PMC3613788
PMID: 23559831
url
https://www.ncbi.nlm.nih.gov/pmc/articles/3613788View
Open Access

Abstract

The semiparametric partially linear model allows flexible modeling of covariate effects on the response variable in regression. It combines the flexibility of nonparametric regression and parsimony of linear regression. The most important assumption in the existing methods for the estimation in this model is to assume a priori that it is known which covariates have a linear effect and which do not. However, in applied work, this is rarely known in advance. We consider the problem of estimation in the partially linear models without assuming a priori which covariates have linear effects. We propose a semiparametric regression pursuit method for identifying the covariates with a linear effect. Our proposed method is a penalized regression approach using a group minimax concave penalty. Under suitable conditions we show that the proposed approach is model-pursuit consistent, meaning that it can correctly determine which covariates have a linear effect and which do not with high probability. The performance of the proposed method is evaluated using simulation studies, which support our theoretical results. A real data example is used to illustrated the application of the proposed method.
 Group selection Semiparametric models Minimax concave penalty Model-pursuit consistency Penalized regression

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