线性误差协变量下部分线性模型的约束统计推断

Restricted statistical inference for partially linear models with error-prone covariates

考虑含有线性误差协变量部分线性模型的统计推断问题。对模型的参数分量,提出了一个线性约束条件下的最小二乘估计,并且证明该估计量满足渐近正态性。同时基于拉格朗日乘子检验方法对约束条件的合理性进行了检验。证明了所提出的检验统计量在原假设成立时渐近服从标准卡方分布。数据模拟表明所提出的估计方法可以有效地消除测量误差对估计精度的影响,并且所提出的检验方法对备择假设是相当敏感的。

The statistical inference for the partially linear models with error-prone covariates were considered.A restrict-ed least square estimation procedure of parametric components was proposed, and the resulting estimator was shown to be asymptotic normality.Moreover, a Lagrange multiplier testing method was proposed to test the validity of the linear restriction.It was proved that the proposed testing statistic follows an asymptotic standard Chi-square distribution under the null hypothesis.Simulation studies imply that the proposed estimation procedure can attenuate the effect of measure-ment errors, and the proposed testing method is more powerful.