Estimation for Varying Coefficient Models with Hierarchical Structure

Feng Li, Yajie Li and Sanying Feng
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Feng Li: School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
Yajie Li: School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
Sanying Feng: School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China

Mathematics, 2021, vol. 9, issue 2, 1-18

Abstract: The varying coefficient (VC) model is a generalization of ordinary linear model, which can not only retain strong interpretability but also has the flexibility of the nonparametric model. In this paper, we investigate a VC model with hierarchical structure. A unified variable selection method for VC model is proposed, which can simultaneously select the nonzero effects and estimate the unknown coefficient functions. Meanwhile, the selected model enforces the hierarchical structure, that is, interaction terms can be selected into the model only if the corresponding main effects are in the model. The kernel method is employed to estimate the varying coefficient functions, and a combined overlapped group Lasso regularization is introduced to implement variable selection to keep the hierarchical structure. It is proved that the proposed penalty estimators have oracle properties, that is, the coefficients are estimated as well as if the true model were known in advance. Simulation studies and a real data analysis are carried out to examine the performance of the proposed method in finite sample case.

Keywords: varying coefficient model; variable selection; interaction term; hierarchical structure; group lasso (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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