Automatic structure discovery for varying-coefficient partially linear models

Guangren Yang, Yanqing Sun, Xia Cui

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Varying-coefficient partially linear models provide a useful tools for modeling of covariate effects on the response variable in regression. One key question in varying-coefficient partially linear models is the choice of model structure, that is, how to decide which covariates have linear effect and which have non linear effect. In this article, we propose a profile method for identifying the covariates with linear effect or non linear effect. Our proposed method is a penalized regression approach based on group minimax concave penalty. Under suitable conditions, we show that the proposed method can correctly determine which covariates have a linear effect and which do not with high probability. The convergence rate of the linear estimator is established as well as the asymptotical normality. The performance of the proposed method is evaluated through a simulation study which supports our theoretical results.

Original languageEnglish (US)
Pages (from-to)7703-7716
Number of pages14
JournalCommunications in Statistics - Theory and Methods
Volume46
Issue number15
DOIs
StatePublished - Aug 3 2017

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Partially Linear Model
Varying Coefficients
Covariates
Nonlinear Effects
Penalized Regression
Linear Estimator
Minimax
Normality
Penalty
Rate of Convergence
Regression
Simulation Study
Modeling

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Cite this

Yang, Guangren ; Sun, Yanqing ; Cui, Xia. / Automatic structure discovery for varying-coefficient partially linear models. In: Communications in Statistics - Theory and Methods. 2017 ; Vol. 46, No. 15. pp. 7703-7716.
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Automatic structure discovery for varying-coefficient partially linear models. / Yang, Guangren; Sun, Yanqing; Cui, Xia.

In: Communications in Statistics - Theory and Methods, Vol. 46, No. 15, 03.08.2017, p. 7703-7716.

Research output: Contribution to journalArticle

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