Variable Selection in Nonparametric and Semiparametric Regression Models

• Main Authors: SU, Liangjun, ZHANG, Yonghui
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2013
• Subjects: Cross validation; High dimensionality; Lasso; Nonparametric regression; Oracle property; Penalized least squares; Penalized likelihood; SCAD; Semiparametric regression; Sparsity; Variable selection; Econometrics; Statistics and Probability
• Online Access: https://ink.library.smu.edu.sg/soe_research/1497; https://ink.library.smu.edu.sg/context/soe_research/article/2496/viewcontent/variable_20selection_20in_20np_20and_20sp20120918.pdf
• Institution: Singapore Management University

This chapter reviews the literature on variable selection in nonparametric and semiparametric regression models via shrinkage. We highlight recent developments on simultaneous variable selection and estimation through the methods of least absolute shrinkage and selection operator (Lasso), smoothly clipped absolute deviation (SCAD) or their variants, but restrict our attention to nonparametric and semiparametric regression models. In particular, we consider variable selection in additive models, partially linear models, functional/varying coefficient models, single index models, general nonparametric regression models, and semiparametric/nonparametric quantile regression models.