Nonparametric Regression Model Based On Penalized Splines

The regression model are normally classified as parametric and non-parametric regression model.For the former,regression function between response and variables is known except the parameters,then the solution of model is just the estimation of parameters.However,when the relation between response and variables cannot be determined,the parametric regression model may not work well.Non-parametric regression model are designed for this cases,in which,the regression functions are not assumed to be some kind of functions,they are constructed by some tools based on the sample points.Then the non-parametric regression models are adaptive to the characters of data and robust for kinds of situations.In this paper,adaptive penalized spline regression models based on radial basis is proposed.Contrast to the traditional penalized spline models,the local weight vector is constructed via the longitudinal ranges of the data over regions around each knot,and it is embedded into the penalized term of the optimal target functions.By this way,different weights are matched to each spline coefficients,which will promote the adaptivity of models.Simultaneously,derivatives of regression functions are estimated using difference quotient.Furthermore,this idea is applied to improve the adaptivity of bivariate thin plate spline models.The simulations and applications show that the new models outperform traditional penalized spline regression model for both univariate and bivariate cases.