In survey sampling, survey data do not necessarily represent the target population, and the samples are often biased. However, information on the survey weights aids in the elimination of selection bias. The Horvitz-Thompson estimator is a well-known unbiased, consistent, and asymptotically normal estimator; however, it is not efficient. Thus, this study derives the semiparametric efficiency bound for various target parameters by considering the survey weight as a random variable and consequently proposes a semiparametric optimal estimator with certain working models on the survey weights. The proposed estimator is consistent, asymptotically normal, and efficient in a class of the regular and asymptotically linear estimators. Further, a limited simulation study is conducted to investigate the finite sample performance of the proposed method. The proposed method is applied to the 1999 Canadian Workplace and Employee Survey data.

翻译：在调查抽样中，调查数据未必能代表目标总体，且样本往往存在偏差。然而，有关调查权重的信息有助于消除选择偏差。霍维茨-汤普森估计量是一种著名的无偏、一致且渐近正态的估计量，但其效率不高。因此，本研究通过将调查权重视为随机变量，推导了各种目标参数的半参数效率界，并据此提出了一种基于调查权重特定工作模型的半参数最优估计量。所提出的估计量在正则渐近线性估计量类中具有一致性、渐近正态性和有效性。此外，本文通过有限模拟研究考察了所提方法的有限样本性能，并将该方法应用于1999年加拿大工作场所与雇员调查数据。