含缺失数据的半参数模型的稳健估计

Robust Estimation of Semi-parametric Models With Missing Data

文章在响应变量随机缺失下,基于分位数回归研究了半参数模型的稳健估计问题。首先基于B样条基函数近似技术,将模型非参数函数的估计问题转化为样条系数向量估计问题;其次,在响应变量随机缺失下,提出了一种新的插补方法,对缺失的响应变量进行多重插补;再次,基于插补后的数据集,构造出新的分位数目标函数,得到模型非参数函数以及参数向量的稳健估计;最后给出了有效算法计算多重插补估计量。通过模拟研究验证了所提方法的有效性和稳健性。

This paper studies the robust estimation of semi-parametric models based on quantile regression with response variables missing at random.First,based on the B-spline basis function approximation technique,the estimation of non-parametric functions in the model is transformed into the estimation of the spline coefficient vectors.Secondly,when the response variables are missing randomly,a new imputation method is proposed to perform multiple imputation for the missing response variables.Then,based on the interpolated data set,a new quantile objective function is constructed to obtain the robust estimators of the non-parametric functions and parameter vectors in the model.Finally,an efficient algorithm is given to calculate the multiple imputation estimator.The effectiveness and robustness of the proposed method are verified by simulation.