Nonresponse frequently arises in practice, and simply ignoring it may lead to erroneous inference. Besides, the number of collected covariates may increase as the sample size in modern statistics, so parametric imputation or propensity score weighting usually leads to estimation inefficiency and introduces a large variability without consideration of sparsity. In this paper, we propose a nonparametric imputation method with sparsity to estimate the finite population mean, where an efficient kernel-based method in the reproducing kernel Hilbet space is employed for estimation and sparse learning. Moreover, an augmented inverse probability weighting framework is adopted to achieve a central limit theorem for the proposed estimator under regularity conditions. The performance of the proposed method is also supported by several simulated examples and one real-life analysis.

实践中经常会出现无响应的情况，忽视它可能会导致错误的推断。此外，在现代统计学中，收集的协变量的数量可能会随着样本量的增加而增加，因此参数插补或倾向得分加权通常会导致估计效率低下，并且在不考虑稀疏性的情况下引入较大的变异性。在本文中，我们提出了一种稀疏性非参数插补方法来估计有限总体均值，其中在再生核希尔贝特空间中采用高效的基于核的方法进行估计和稀疏学习。此外，采用增强逆概率加权框架来实现所提出的估计器在规律性条件下的中心极限定理。该方法的性能还得到了几个模拟示例和一项现实分析的支持。