Robust functional coefficient selection for the single-index varying coefficients regression model

ABSTRACT

A rank-based estimation and selection of the functional regression coefficients for the single-index varying coefficient regression model is considered. The estimation of the functional regression coefficients together with the selection procedure are carried out following a proposed back-fitting type computational algorithm by minimizing the rank-based objective function. Finite sample performance of the proposed estimator are evaluated via extensive Monte Carlo simulation studies. These demonstrate the robustness and efficiency of the proposed estimator compared to its least squares counterpart under different settings of the model error distribution. A real data example motivated by problems in deep-water fish ecology is given to illustrate the proposed methodology.

Keywords:

• Group Lasso
• model selection
• nonparametric estimation
• rank pseudo-norm
• semi-parametric models

2010 Mathematics Subject Classifications:

• 62J02
• 62G05
• 62F12
• 62G20

Disclosure statement

No potential conflict of interest was reported by the author(s).