Statistical inference with non-probability survey samples is an emerging topic in survey sampling and official statistics and has gained increased attention from researchers and practitioners in the field. Much of the existing literature, however, assumes that the participation mechanism for non-probability samples is ignorable. In this paper, we develop a pseudo-likelihood approach to estimate participation probabilities for nonignorable non-probability samples when auxiliary information is available from an existing reference probability sample. We further construct three estimators for the finite population mean using regression-based prediction, inverse probability weighting (IPW), and augmented IPW estimators, and study their asymptotic properties. Variance estimation for the proposed methods is considered within the same framework. The efficiency of our proposed methods is demonstrated through simulation studies and a real data analysis using the ESPACOV survey on the effects of the COVID-19 pandemic in Spain.

翻译：非概率调查样本的统计推断是抽样调查与官方统计领域的新兴课题，正日益受到该领域研究者与实践者的关注。然而，现有文献大多假设非概率样本的参与机制是可忽略的。本文提出了一种伪似然方法，用于在存在参考概率样本提供辅助信息的情况下，估计不可忽略非概率样本的参与概率。我们进一步构建了基于回归预测、逆概率加权（IPW）以及增强逆概率加权估计量的三种有限总体均值估计量，并研究了它们的渐近性质。在同一框架下考虑了所提方法的方差估计问题。通过模拟研究及基于西班牙COVID-19疫情影响调查（ESPACOV）的实际数据分析，验证了所提方法的有效性。