Resampling-based efficient shrinkage method for non-smooth minimands

In many regression models, the coefficients are typically estimated by optimising an objective function with a U-statistic structure. Under such a setting, we propose a simple and general method for simultaneous coefficient estimation and variable selection. It combines an efficient quadratic approximation of the objective function with the adaptive lasso penalty to yield a piecewise-linear regularisation path which can be easily obtained from the fast lars-lasso algorithm. Furthermore, the standard asymptotic oracle properties can be established under general conditions without requiring the covariance assumption (Wang, H., and Leng, C. (2007), Unified Lasso Estimation by Least Squares Approximation', Journal of the American Statistical Association, 102, 1039-1048). This approach applies to many semiparametric regression problems. Three examples are used to illustrate the practical utility of our proposal. Numerical results based on simulated and real data are provided.