Nonresponse after probability sampling is a universal challenge in survey sampling, often necessitating adjustments to mitigate sampling and selection bias simultaneously. This study explored the removal of bias and effective utilization of available information, not just in nonresponse but also in the scenario of data integration, where summary statistics from other data sources are accessible. We reformulate these settings within a two-step monotone missing data framework, where the first step of missingness arises from sampling and the second originates from nonresponse. Subsequently, we derive the semiparametric efficiency bound for the target parameter. We also propose adaptive estimators utilizing methods of moments and empirical likelihood approaches to attain the lower bound. The proposed estimator exhibits both efficiency and double robustness. However, attaining efficiency with an adaptive estimator requires the correct specification of certain working models. To reinforce robustness against the misspecification of working models, we extend the property of double robustness to multiple robustness by proposing a two-step empirical likelihood method that effectively leverages empirical weights. A numerical study is undertaken to investigate the finite-sample performance of the proposed methods. We further applied our methods to a dataset from the National Health and Nutrition Examination Survey data by efficiently incorporating summary statistics from the National Health Interview Survey data.

翻译：概率抽样后的无应答问题是调查抽样中的普遍挑战，通常需要同时调整以减轻抽样偏差和选择偏差。本研究不仅探讨了在无应答情景下消除偏差并有效利用可用信息，还拓展至数据整合场景——即当其他数据源的汇总统计量可获取时的处理。我们将这些情景重构为两步单调缺失数据框架：第一步缺失源于抽样过程，第二步缺失源于无应答。随后，推导了目标参数的半参数效率界，并提出了基于矩方法和经验似然方法的自适应估计器以实现该下界。所提估计量兼具高效性和双重稳健性。然而，自适应估计器实现效率需要对某些工作模型进行正确设定。为增强对工作模型错误设定的稳健性，我们通过提出一种有效利用经验权重的两步经验似然法，将双重稳健性扩展为多重稳健性。通过数值研究考察了所提方法的有限样本性能，并进一步将方法应用于国家健康与营养调查数据，通过高效整合国家健康访谈调查数据的汇总统计量进行实证分析。