A Lasso-Type Approach for Estimation and Variable Selection in Single Index Models

The single index model is a natural extension of the linear regression model for applications in which linearity does not hold. In this article, we propose a penalized local linear smoothing method, called sim-lasso, for estimation and variable selection under the single index model. The sim-lasso method penalizes the derivative of the link function and thus can be considered an extension of the usual lasso. Computational algorithms are developed for calculating the sim-lasso estimates and solution paths. The properties of the solution paths are also investigated. Simulation study and real data application demonstrate the excellent performance of the sim-lasso method. Supplemental materials for the article are available online.