Double Penalized Semi-Parametric Signed-Rank Regression with Adaptive LASSO

Abstract

In this paper, a semi-parametric regression model with an adaptive LASSO penalty imposed on both the linear and the nonlinear components of the mode is considered. The model is rewritten so that a signed-rank technique can be used for estimation. The nonlinear part consists of a covariate that enters the model nonlinearly via an unknown function that is estimated using B-splines. The author shows that the resulting estimator is consistent under heavy-tailed distributions and asymptotic normality results are given. Monte Carlo simulations as well as practical applications are studied to assess the validity of the proposed estimation method.