Concave group methods for variable selection and estimation in high-dimensional varying coefficient models

Guang Ren Yang, Jian Huang, Yong Zhou

Research output: Contribution to journalArticle

Abstract

The varying-coefficient model is flexible and powerful for modeling the dynamic changes of regression coefficients. We study the problem of variable selection and estimation in this model in the sparse, high-dimensional case. We develop a concave group selection approach for this problem using basis function expansion and study its theoretical and empirical properties. We also apply the group Lasso for variable selection and estimation in this model and study its properties. Under appropriate conditions, we show that the group least absolute shrinkage and selection operator (Lasso) selects a model whose dimension is comparable to the underlying model, regardless of the large number of unimportant variables. In order to improve the selection results, we show that the group minimax concave penalty (MCP) has the oracle selection property in the sense that it correctly selects important variables with probability converging to one under suitable conditions. By comparison, the group Lasso does not have the oracle selection property. In the simulation parts, we apply the group Lasso and the group MCP. At the same time, the two approaches are evaluated using simulation and demonstrated on a data example.

Original languageEnglish (US)
Pages (from-to)2073-2090
Number of pages18
JournalScience China Mathematics
Volume57
Issue number10
DOIs
StatePublished - Oct 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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