通过校准估计响应概率的抽样推断
Inference from Sampling with Response Probabilities Estimated via Calibration
AI总结：
该研究构建通用框架比较校准法与极大似然法估计响应概率的抽样推断效果，证明校准法所得估计量渐近无偏、具双重稳健性且有效率增益，还分析了相关估计问题并通过模拟验证。
摘要：
控制无应答偏差的一种解决方案是将应答者的设计权重乘以估计响应概率的倒数，以补偿无应答者的影响。极大似然法和校准法是可用于获得估计响应概率的两种方法。我们构建了一个可对这两种方法进行比较的通用框架，并针对采用校准法时所得估计量的行为开展了渐近研究，研究假设响应概率服从逻辑回归模型，数据满足随机缺失假设且为非聚类数据。本研究有三项主要贡献：1）证明了通过校准估计响应概率得到的估计量渐近等价于无偏估计量，且与使用真实响应概率的估计量相比，通过校准估计响应概率可获得效率增益；2）证明了通过校准估计响应概率得到的估计量对模型误设具有双重稳健性，并解释了采用极大似然法时无法保证双重稳健性的原因；3）讨论并阐释了与响应概率估计相关的问题，即估计方程解的存在性、收敛问题以及极端权重问题，解释并说明了上述第一个问题在校准法中比在极大似然估计中更易出现的原因。我们还呈现了一项模拟研究的结果，以对上述内容进行例证说明。
英文摘要：
A solution to control for nonresponse bias consists of multiplying the design weights of respondents by the inverse of estimated response probabilities to compensate for the nonrespondents. Maximum likelihood and calibration are two approaches that can be applied to obtain estimated response probabilities. We consider a common framework in which these approaches can be compared. We develop an asymptotic study of the behavior of the resulting estimator when calibration is applied. A logistic regression model for the response probabilities is postulated. Missing at random and unclustered data are supposed. Three main contributions of this work are: 1) we show that the estimators with the response probabilities estimated via calibration are asymptotically equivalent to unbiased estimators and that a gain in efficiency is obtained when estimating the response probabilities via calibration as compared to the estimator with the true response probabilities, 2) we show that the estimators with the response probabilities estimated via calibration are doubly robust to model misspecification and explain why double robustness is not guaranteed when maximum likelihood is applied, and 3) we discuss and illustrate problems related to response probabilities estimation, namely existence of a solution to the estimating equations, problems of convergence, and extreme weights. We explain and illustrate why the first aforementioned problem is more likely with calibration than with maximum likelihood estimation. We present the results of a simulation study in order to illustrate these elements.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
