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B spline variable selection for the single index models

Jianbo Li (), Yuan Li and Riquan Zhang
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Jianbo Li: Guangzhou University
Yuan Li: Guangzhou University
Riquan Zhang: East China Normal University

Statistical Papers, 2017, vol. 58, issue 3, 691-706

Abstract: Abstract Through the nonconcave penalized least squares method, we consider the variable selection in the full nonparametric regression models with the B spline-based single index approximation. Under some regular conditions, we show that the resulting estimates with SCAD and HARD thresholding penalties enjoy $$\sqrt{n}$$ n -consistency and oracle properties. We use some simulation studies and a real example to illustrate the performance of our proposed variable selection procedure.

Keywords: Single index model; Lasso; SCAD; Hard Thresholding; Oracle; Primary 62G08; Secondary 62H12 (search for similar items in EconPapers)
Date: 2017
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