We address the weighting problem in voluntary samples under a nonignorable sample selection model. Under the assumption that the sample selection model is correctly specified, we can compute a consistent estimator of the model parameter and construct the propensity score estimator of the population mean. We use the empirical likelihood method to construct the final weights for voluntary samples by incorporating the bias calibration constraints and the benchmarking constraints. Linearization variance estimation of the proposed method is developed. A limited simulation study is also performed to check the performance of the proposed methods.

翻译：我们探讨了在不可忽略样本选择模型下自愿样本的加权问题。假设样本选择模型被正确设定，我们可以计算模型参数的一致估计量，并构建总体均值的倾向得分估计量。我们利用经验似然方法，通过引入偏差校准约束和基准约束来构建自愿样本的最终权重。同时，我们开发了所提出方法的线性化方差估计。此外，还进行了有限的模拟研究，以检验所提出方法的性能。