Automatic Variable Selection for Partially Linear Functional Additive Model and Its Application to the Tecator Data Set. (16th August 2018)

• Record Type: Journal Article
• Authors: Hu, Yuping; Feng, Sanying; Xue, Liugen
• Other Names: Cortés J.-C. Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2018(2018)
• Publication Date: 2018-08-16
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2018/5683539
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : We introduce a new partially linear functional additive model, and we consider the problem of variable selection for this model. Based on the functional principal components method and the centered spline basis function approximation, a new variable selection procedure is proposed by using the smooth-threshold estimating equation (SEE). The proposed procedure automatically eliminates inactive predictors by setting the corresponding parameters to be zero and simultaneously estimates the nonzero regression coefficients by solving the SEE. The approach avoids the convex optimization problem, and it is flexible and easy to implement. We establish the asymptotic properties of the resulting estimators under some regularity conditions. We apply the proposed procedure to analyze a real data set: the Tecator data set.