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. The paper develops asymptotic properties of the resulting estimator when calibration is applied. A logistic regression model for the response probabilities is postulated and missing at random data is supposed. The author shows 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.

翻译：一种控制无应答偏差的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。极大似然法和校准法是两种可用于获得估计响应概率的方法。本文研究了应用校准法时所得估计量的渐近性质。本文假设响应概率服从逻辑回归模型，并假定数据是随机缺失的。作者表明，通过校准法估计响应概率得到的估计量渐近等价于无偏估计量，并且与使用真实响应概率的估计量相比，通过校准法估计响应概率可获得效率提升。