协变量缺失下基于诱导光滑方法的加权分位数回归

摘要

在部分协变量随机缺失机制下的分位数回归模型中，提出回归参数的诱导光滑加权估计及其渐近协方差估计，证明了诱导光滑加权估计和经验似然加权估计有相同的渐近协方差，且诱导光滑加权估计的渐近协方差估计也是相合的，并给出了诱导光滑加权估计及其渐近协方差估计的高效算法。模拟结果表明，新方法在有限样本下表现优良。%We proposed an induced smoothing-based weighted estimator of regression parameter and an estimator of its asymptotic covariance in quantile regression model of partial covariates with random missing mechanism.We showed that the induced smoothing-based weighted estimator and empirical likelihood-based weighted estimator had the same asymptotic covariance and the estimator of the asymptotic covariance of the induced smoothing-based weighted estimator was also consistent.We gave an efficient algorithm for calculating the induced smoothing-based weighted estimator of regression parameter and the estimator of its asymptotic covariance.Simulation results show that the proposed method performs well in finite samples.