基于两步样条光滑法的非参数回归模型研究

Study on Nonparametric Regression Model Based on Two-step Spline Smoothing

条件方差函数及其同时置信带是非参数回归领域的研究热点之一,文章针对重节点数据,基于自然三次样条基和B样条基建立两步样条光滑法模型,利用非参数bootstrap方法,借鉴Song和Yang(2009)的思路,构造条件方差函数及其置信带;在此模型基础上,进行加权迭代改进,建立加权迭代自然三次样条模型和加权迭代B样条模型,基于置信带覆盖率评估模型优劣。研究表明,加权迭代改进可以提高条件方差函数及其同时置信带的覆盖率;交叉检验函数敏感性较差,根据经验选择光滑参数具有可行性;B样条模型以牺牲少量的拟合优度为代价,极大地提高运算速度。

Conditional variance function and its simultaneous confidence band are one of the research hotspots in the field of nonparametric regression.This paper aims at the heavy node data and relies on natural cubic spline base and B-spline base to establish the two-step spline smoothing model.Then the paper uses the non-parametric bootstrap method and draws on the ideas of Song and Yang(2009)to construct the conditional variance function and its confidence band,on the basis of which to make the weighted iterative improvement,and to establish the weighted iterative natural cubic spline model and the weighted iterative B-spline model.Finally,the paper evaluates model strengths and weaknesses based on confidence band coverage.The results show that the weighted iterative improvement can increase the coverage of the conditional variance function and its simultaneous confidence band;the cross test function has poor sensitivity,and it is feasible to select smooth parameters according to experience;B-spline model greatly improves the operation speed at the expense of a little goodness of fit.