Nonparametric Estimation of Mean Functionals with Data Missing at Random
本文提出一种无需参数假设的估计方法，用于处理调查中常见的双抽样缺失数据，通过核回归估计均值，并在随机缺失假设下推导渐近分布，适用于非随机观察性研究中的平均处理效应估计。
Abstract This article considers a distribution-free estimation procedure for a basic pattern of missing data that often arises from the wellknown double sampling in survey methodology. Without parametric modeling of the missing mechanism or the joint distribution, kernel regression estimators are used to estimate mean functionals through empirical estimation of the missing pattern. A generalization of the method of Cheng and Wei is verified under the assumption of missing at random. Asymptotic distributions are derived for estimating the mean of the incomplete data and for estimating the mean treatment difference in a nonrandomized observational study. The nonparametric method is compared with a naive pairwise deletion method and a linear regression method via the asymptotic relative efficiencies and a simulation study. The comparison shows that the proposed nonparametric estimators attain reliable performances in general.