Statistical analysis of voluntary survey data is an important area of research in survey sampling. We consider a unified approach to voluntary survey data analysis under the assumption that the sampling mechanism is ignorable. Generalized entropy calibration is introduced as a unified tool for calibration weighting to control the selection bias. We first establish the relationship between the generalized calibration weighting and its dual expression for regression estimation. The dual relationship is critical in identifying the implied regression model and developing model selection for calibration weighting. Also, if a linear regression model for an important study variable is available, then two-step calibration method can be used to smooth the final weights and achieve the statistical efficiency. Asymptotic properties of the proposed estimator are investigated. Results from a limited simulation study are also presented.

翻译：自愿性调查数据的统计分析是抽样调查领域的重要研究方向。本文在抽样机制可忽略的假设下，提出一种针对自愿性调查数据的统一分析方法。广义熵校准被引入作为校准加权的统一工具，以控制选择偏差。我们首先建立了广义校准加权与其回归估计对偶表达式之间的关系。该对偶关系对于识别隐含回归模型及开发校准加权的模型选择方法至关重要。此外，若可获得重要研究变量的线性回归模型，则可采用两步校准方法对最终权重进行平滑处理以实现统计有效性。本文研究了所提估计量的渐近性质，并展示了有限模拟研究的结果。