Weighting in survey analysis under informative sampling
Weighting in survey analysis under informative sampling
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DOI：
10.1093/biomet/ass085
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发表时间：
2013-06-01
期刊：
影响因子：
2.7
通讯作者：
Skinner, C. J.
中科院分区：
文献类型：
--
作者：
Kim, Jae Kwang;Skinner, C. J.
在以协变量为条件的回归分析中，与结果变量相关的抽样称为信息抽样，这可能导致普通最小二乘估计的偏倚。通过纳入概率的倒数进行加权大致消除了这种偏倚，但可能会扩大方差。本文研究了两种方法来修改这样的权重，以提高效率，同时保持一致性。一种方法是将逆概率权重乘以协变量的函数。第二种是平滑结果变量和协变量的给定值的权重。探讨了这两种方法构造权重的最佳方法。这两种方法都需要辅助权重模型的拟合。研究了所得估计的渐近性质，得到了线性化方差估计。将该方法推广到广义线性模型的伪极大似然估计。不同的加权估计的性质进行了比较，在有限的模拟研究。讨论了估计量对辅助权重模型或回归模型误设定的鲁棒性。
Sampling related to the outcome variable of a regression analysis conditional on covariates is called informative sampling and may lead to bias in ordinary least squares estimation. Weighting by the reciprocal of the inclusion probability approximately removes such bias but may inflate variance. This paper investigates two ways of modifying such weights to improve efficiency while retaining consistency. One approach is to multiply the inverse probability weights by functions of the covariates. The second is to smooth the weights given values of the outcome variable and covariates. Optimal ways of constructing weights by these two approaches are explored. Both approaches require the fitting of auxiliary weight models. The asymptotic properties of the resulting estimators are investigated and linearization variance estimators are obtained. The approach is extended to pseudo maximum likelihood estimation for generalized linear models. The properties of the different weighted estimators are compared in a limited simulation study. The robustness of the estimators to misspecification of the auxiliary weight model or of the regression model of interest is discussed.