半参数回归模型及模拟实例分析

Semiparametric Regression Model with Simulation

目的 放宽经典线性模型中的解释变量的线性假定和探讨半参数回归分析模型。方法 利用最小惩罚二乘原理构造加权惩罚平方和 ,通过广义交互有效得分函数自动选择光滑参数值 ,用直接法求解方程组。结果 用SAS程序实现了半参数回归分析 ,得到了回归系数向量和样条函数的最小惩罚二乘估计 ,模拟实例表明 ,半参数回归模型较传统的线性模型有较强的适应性。结论 半参数回归模型是经典线性模型和非参数回归模型的一个混合体 ,可作为回归分析的一种新技术得到广泛应用。

Objective To relax linear assumption of explanatory variable in classical linear model and explore semiparametric regression model.Methods Based on penalized least squares,the penalized weighted sum of squares is set up.The choice of smoothing parameter can be obtained automatically by using generalized cross-validation score and equation set can be solved.Results The penalized least squares estimator for regression coefficient vector and spline function can be got by submitting SAS programs in semiparmetric regression analysis,and the adaptation of this technique is more flexible than the traditional linear model,along with statistical simulation.Conclusion The semiparametric regression model would be a combine of classical linear model with nonparametric regression model,It would be widely used in various research fields as a new regression analysis technique.