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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 利用三次样条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LS法 ,可作为曲线拟合的一种优异方法得到广泛应用。
Objective To improve the classical least squares estimation method for regression analysis and explore the nonparametric regression analysis method for smooth splines. Methods The organic combination of cubic spline function and roughness penalty method was used to construct the penalty sum of squares. The smooth parameter value was automatically selected by the generalized interactive effective score function and pattern search method. Results The non-parametric regression analysis of smooth spline was implemented by SAS program. The minimum penalty quadratic estimate of the regression function was obtained. The examples show that this method is superior to the traditional method and non-parametric Mononotic regression. Conclusion The non-parametric regression analysis method can optimize both the goodness-of-fitness and the smoothness, and improves the classical LS method. It can be widely used as an excellent method for curve fitting.