Cost-effective survey methods such as multi(R)-phase sampling typically generate samples that are collections of monotonic subsamples, i.e., the variables observed for the units in subsample r are also observed for the units in subsample r + 1 for r = 1,…,R – 1. These subsamples represent subpopulations that can be systematically different if the selection of a unit in each phase of sampling depends on the observed variables for that unit from past phases. Our article is about optimally combining all the subsamples for the efficient estimation of a finite dimensional parameter defined by moment restrictions on a generic target population that is an arbitrary union of these subpopulations. Only the R-th subsample is assumed to contain all the variables that are arguments of the moment function. Semiparametric efficiency bounds for estimation are obtained under a unified framework, allowing for full generality of the selection on observables in the sampling design. Contribution of each subsample toward efficient estimation is analyzed; and this turns out to differ fundamentally from that in setups where the same collection of subsamples is instead generated unplanned by unknown sampling. Uniquely, our setup enables all the subsamples to contribute to the efficient estimation for all the target populations, which we show is not possible in other setups. Efficient estimation is standard. Simulation evidence of substantive efficiency gains from using all the subsamples is provided for all the targets.

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关于从多个不完整子样本中获得的效率

具有成本效益的调查方法，例如多（R) 阶段采样通常会生成作为单调子样本集合的样本，即为子样本中的单位观察到的变量r也观察到子样本中的单位r+ 1 为r= 1,…,R– 1. 如果在每个抽样阶段选择一个单位取决于该单位从过去阶段观察到的变量，则这些子样本代表的子群体可能会系统地不同。我们的文章是关于优化组合所有子样本，以有效估计有限维参数，该参数由对作为这些子总体的任意联合的通用目标总体的矩限制定义。只有R-th 子样本假定包含所有作为矩函数参数的变量。估计的半参数效率界限是在一个统一的框架下获得的，允许在抽样设计中对可观察量的选择具有完全的普遍性。分析每个子样本对有效估计的贡献；事实证明，这与设置相同的子样本集合是由未知采样计划外生成的设置有根本的不同。独特的是，我们的设置使所有子样本能够为所有目标群体的有效估计做出贡献，我们证明这在其他设置中是不可能的。有效的估计是标准的。为所有目标提供了使用所有子样本带来的实质性效率增益的模拟证据。