Sparse Semi-Functional Partial Linear Single-Index Regression

Abstract

The variable selection problem is studied in the sparse semi-functional partial linear model, with single-index type influence of the functional covariate in the response. The penalized least squares procedure is employed for this task. Some properties of the resultant estimators are derived: the existence (and rate of convergence) of a consistent estimator for the parameters in the linear part and an oracle property for the variable selection method. Finally, a real data application illustrates the good performance of our procedure.