Two Nonparametric Regression Models With Local Weights

Traditional penalized spline regression models use B-spline basis to fitting regression functions and adopts penalties from the second differences of spline coefficients to get the trade-off bet,ween goodness of fit and roughness.Support vector quantile regression models map input space to feature space by a kernel function,use the check function as loss and the norm of estimate as penalty to get optimal target functions.However,the penalty weights in this two models are identical along with the explain variable,this leads to an unsatisfied estimation when the data is changing heterogeneously.In this paper,penalties adjusted by local weights are constructed and applied to improve the adaptability of this t,wo models.First,inspired by the "adaptive lasso",a monotone decreasing function of the pre-estimates of spline coefficients is used for penalized spline regression models.Second,in the support vector quantile regression models,a monotone decreasing function via the variances of local observations of response variable are used to construct weights,which helps the fitting to match the changing characteristics of data.Simulations and applications show that the new models outperform the old ones by smaller mean squared errors and mean absolute errors.