部分线性可加模型的随机约束岭估计

A Stochastic Restricted Ridge Estimator in Partially Linear Additive Models

本文研究了部分线性可加模型这类半参数模型在线性部分自变量存在多重共线性,同时还附加有随机约束条件时的估计问题。基于针对半参数模型的Profile最小二乘技术,处理多重共线性问题的岭估计方法以及针对随机约束的混合估计技术,构造了参数分量的随机约束岭估计,给出了估计量的偏与协方差,并给出了所提估计量的渐近性质。最后通过数值模拟验证了所提估计方法的表现。

This paper studies the estimation of a partially linear additive model when there are stochastic linear restrictions on the parameter components and multicollinearity problem exists, simultaneously. Based on the profile least square method of semiparametric model, ridge estimation approach for multicollinearity problem and mixed estimation technique for stochastic restrictions, a stochastic ridge estimator for the parametric components was proposed and its bias and covariance were provided. Meanwhile, the asymptotic distribution of this proposed estimator has also been proved. Finally, some simulations are carried out to study the finite properties of the proposed estimator.