线性约束下纵向数据部分线性模型的估计  

Estimation of Partially Linear Models for Longitudinal Data under Linear Constraints

作　　者：冯彬娟 童画 袁德美[1] FENG Binjuan;TONG Hua;YUAN Demei(School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067

出　　处：《重庆工商大学学报（自然科学版）》2024年第6期87-93,共7页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：重庆市自然科学基金(CSTB2022NSCQ-MSX1370)。

摘　　要：目的 研究纵向数据部分线性模型的参数和未知回归函数的估计问题。方法 考虑在一些统计应用中,模型参数通常带有一定的约束,提出一种基于约束最小二乘与二次光滑局部线性估计的方法。该方法首先利用profile最小二乘法和Lagrange乘数法得到参数和回归函数的约束,即profile最小二乘估计量;再结合改进的二次光滑局部线性估计方法得到约束条件下模型的最终估计,并在一定正则条件下,证明了所构造的参数和回归函数估计量的渐近正态性;同时,通过数值模拟得到了有约束和无约束两种情况下参数分量的偏差、标准差和均方误差,并绘制了两种情况下回归函数的拟合曲线,验证了上述方法的有效性。结果 模拟结果表明:相对于不考虑约束条件的估计量,考虑约束条件的估计量具有更高的估计精度;回归函数的拟合曲线展现出了良好的拟合效果,进一步验证了所提出估计方法的有效性。结论 在实际研究中,通常可以获取参数分量的一些额外信息,充分利用这些信息能够提高估计的准确性;与无约束的估计方法相比,带有约束的估计方法能使估计的效率得到提高。Objective The estimation of parameters and unknown regression functions in partially linear models for longitudinal data was investigated.Methods Considering that model parameters often have certain constraints in some statistical applications,a method based on constrained least squares and quadratic smoothing local linear estimation was proposed.This method first utilized profile least squares and the Lagrange multiplier method to obtain constrained profile least squares estimators for parameters and regression functions.Then,combined with an improved quadratic smoothing local linear estimation method,the final estimation of the model under constraints was obtained.Under certain regularity conditions,the asymptotic normality of the constructed parameters and the estimators of the regression function was proved.Meanwhile,through numerical simulations,the biases,standard deviations,and mean square errors of parameter components under both constrained and unconstrained situations were obtained.The fitting curves of regression functions under both situations were plotted to verify the effectiveness of the proposed method.Results Simulation results showed that compared with estimators without considering constraints,estimators considering constraints had higher estimation accuracy.The fitting curves of regression functions demonstrated good fitting effects,further confirming the effectiveness of the proposed estimation method.Conclusion In practical research,additional information about parameter components can often be obtained,and fully utilizing this information can improve estimation accuracy.Compared with unconstrained estimation methods,constrained estimation methods can improve estimation efficiency.

关 键 词：纵向数据 部分线性模型 约束估计 profile最小二乘 二次光滑估计 

分 类 号：O212.7[理学—概率论与数理统计]