Variable selection in partially linear additive models for modal regression

ABSTRACT

Based on B-spline basis functions and smoothly clipped absolute deviation (SCAD) penalty, we present a new estimation and variable selection procedure based on modal regression for partially linear additive models. The outstanding merit of the new method is that it is robust against outliers or heavy-tail error distributions and performs no worse than the least-square-based estimation for normal error case. The main difference is that the standard quadratic loss is replaced by a kernel function depending on a bandwidth that can be automatically selected based on the observed data. With appropriate selection of the regularization parameters, the new method possesses the consistency in variable selection and oracle property in estimation. Finally, both simulation study and real data analysis are performed to examine the performance of our approach.

KEYWORDS:

• B-spline
• Modal regression
• Oracle property
• Partially linear additive models
• Robust estimation

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62G10
• Secondary 62G08