Mixed degree regression function estimation using weighted lasso penalty

Abstract

We consider a nonparametric function estimation method with mixed degree using weighted lasso penalty. The ℓ₁ norm penalty controls linear and cubic trends depending on the value of the parameter. In the proposed estimator, we introduce one computational algorithm for constrained convex optimization problems corresponding to the Lagrangian dual problem based on quadratic programming. Subsequently, using simulations and two real data analyses, numerical studies are conducted to verify the performance of the estimator of the proposed method by identifying the relationship between the data.