title: Semiparametric Regression Pursuit.
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.
authors.affiliation: University of Iowa.
authors.forename: Jian
authors.initials: J
authors.lastname: Huang
authors.forename: Fengrong
authors.initials: F
authors.lastname: Wei
authors.forename: Shuangge
authors.initials: S
authors.lastname: Ma
keywords: Group selection; Minimax concave penalty; Model-pursuit consistency; Penalized regression; Semiparametric models
references.citation: Stat Methods Med Res. 1995 Sep;4(3):187-96
references.pmid: 8548102
references.citation: Ann Appl Stat. 2011 Jan 1;5(1):232-253
references.pmid: 22081779
references.citation: J Am Stat Assoc. 2011 Sep 1;106(495):1099-1112
references.pmid: 22121305
references.citation: South Med J. 1997 Aug;90(8):814-20
references.pmid: 9258308
references.citation: Ann Stat. 2010 Aug 1;38(4):2282-2313
references.pmid: 21127739