随机缺失数据下样本分位数估计

Sample Quantile Estimation for Ignorable Nonresponse

分位数的估计在生物医学、社会经济调查等领域有着广泛的应用,然而在实际问题的研究中,往往由于各种人为或不可控因素造成数据收集不完全.本文在随机缺失(MAR)假设条件下,利用非参数核补法和局部多重插补法给出了响应变量缺失时样本分位数的估计,并利用经验过程等理论证明了由这两种方法得到的分位数估计的大样本性质,同时,使用重抽样方法给出了估计的渐近方差的估计,模拟结果验证了这两种方法的有效性.文章所提两种方法的优点在于:首先,所提出的缺失修正方法不需要对缺失概率的模型做任何假设;其次,方法亦适用于其他有关参数不可微的估计目标函数;最后,方法很容易地推广到一般M估计的情况,并可以对多个分位数同时进行估计.

Quantile estimation is widely used in clinical trials, social statistics and economies. In practise, complete data are often not available for every subject due to many reasons. In this article, we study the estimation of sample quantiles of response under missing at random assumption. We use noparametric kernel regression imputation method and local multiple imputation method to estimate sample quan- tiles. Asymptotic properties are also established and a revised bootstrap method is proposed to estimate the asymptotic variance of the two estimators. Simulation stud- ies are reported to assess the finite sample properties of the proposed estimators. The merit of our methods are that, firstly, we don＇t need to give any assumptions on the missing response model; secondly, our method can deal with other non-differentiable estimation functions; finally, our method can be extended to solve other M estimator, and can estimate several quantiles simultaneously.