光滑样条非参数回归方法及医学应用

目的 改进回归分析的经典最小二乘估计方法和探讨光滑样条非参数回归分析方法。方法 利用三次函数和粗糙度惩罚方法的有机结合,构造惩罚平方和,通过广义交互有效得分函数和模式搜索法自动选择光滑参数值。结果 用ＳＡＳ程序实现了光滑样条非参数回归分析,得到了回归函数的最小惩罚二乘估计,实例表明,该方法优于传统方法和非参数Ｍｏｎｏｔｏｎｉｃ回归。结论 非参数回归分析方法能够最佳地兼顾拟合优度和光滑度,改进了经典

Nonparametric Smoothing Spline Regression Analysis with Its Application in Medicine

Objective To improve on classical least squares estimate of regression analysis and explore nonparametric smoothing spline regression analysis.Methods Based on cubic spline function and roughness penalty approach,the penalized sum of squares is set up.The choice of smoothing parameter can be obtained automatically by using generalized cross validation score and a module form search method.Results The penalized least squares estimator for regression function can be got by submitting SAS programs in nonparametric smoothing spline regression analysis,and the technique is apparently better than the traditional method and nonparametric monotonic regression,along with an example.Conclusion The technique of nonparametric regression analysis would compromise between goodness of fit and smoothness,and improve on classical LS method.It would be widely used in various research fields as an excellent method.