Sparse structure selection and estimation

ABSTRACT

This paper studies the sparsity selection and estimation in nonparametric additive models. The sparsity refers to two types — across and within variables. Sparsity across variables corresponds to the irrelevant components in the models; sparsity within variables corresponds to zero function values over the sub-domains of the relevant components. To select and estimate the sparsity, I approximate each component by B-splines and propose a group bridge penalized method, which can simultaneously identify the zero functions and zero structures of the nonzero functions. Simulation studies demonstrate the effectiveness of the proposed method in sparsity selection and estimation across and within variables.

Keywords:

• Across and within variables
• Additive model
• Sparse structure

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G05
• 62G08
• 62H99