带有缺失协变量的分位数回归模型的参数估计

Parameter Estimation of Quantile Regression Model With Missing Covariates

数据挖掘的常用方法是回归分析,传统的回归分析仅可由自变量估计因变量的条件期望,分位数回归可由自变量估计因变量的条件分位数。在实际应用中,常会因为某些原因导致数据缺失,这些数据不可盲目删除或丢弃,否则会造成有偏的估计。在分位数回归模型下,文章以缺失数据为研究对象,主要解决两个方面的问题:一是利用逆概率加权的方法设计权重,通过构造加权的估计函数调整协变量随机缺失对参数估计造成的影响;二是设计Proximal-ADMM算法对模型参数进行估计。模拟与实证研究表明:采用Proximal-ADMM算法对带有缺失数据的分位数回归模型进行参数优化,所得估计量是无偏的。

The common method of data mining is regression analysis. The traditional regression analysis only estimates conditional expectations of dependent variables from independent variables, and quantile regression can estimate conditional quantiles of dependent variables from independent variables. In practical application, data is often missing due to some reasons. The data cannot be deleted or discarded blindly, otherwise biased estimation would be caused. Under the quantile regression model,this paper takes the missing data as the research object and mainly solves two problems: Firstly, the inverse probability weighting method is used to design weights, and the weighted estimation function is constructed to adjust the impact of random missing of covariates on parameter estimation. Secondly, the Proximal-ADMM algorithm is designed to estimate the model parameters. Simulations and empirical studies show that unbiased is the estimator obtained by using Proximal-ADMM algorithm to optimize the parameters of the quantile regression model with missing data.