The granting process is based on the probability that the applicant will refund his/her loan given his/her characteristics. This probability, also called score, is learnt based on a dataset in which rejected applicants are excluded. Thus, the population on which the score is used is different from the learning population. Many “reject inference” methods try to exploit the data available from the rejected applicants in the learning process. However, most of these methods are empirical and lack of formalization of their assumptions, and of their expected theoretical properties. We formalize such hidden assumptions in a general missing data setting for some of the most common reject inference methods. It reveals that hidden modelling is mostly incomplete, thus prohibiting to compare existing methods within the general model selection mechanism (except by financing “non-fundable” applicants). So, we assess performance of the methods on both simulated data and real data (from CACF, a major European loan issuer). Unsurprisingly, no method seems uniformly dominant. Both these theoretical and empirical results not only reinforce the idea to carefully use the classical reject inference methods but also to invest in future research works for designing model-based reject inference methods (without financing “non-fundable” applicants).

授予过程是基于申请人考虑到他/她的特征而退还他/她的贷款的可能性。这个概率，也称为分数，是根据排除被拒绝申请人的数据集来学习的。因此，使用分数的人群与学习人群不同。许多“拒绝推理”方法试图在学习过程中利用被拒绝申请人的可用数据。然而，这些方法中的大多数都是经验性的，缺乏对其假设的形式化，以及它们的预期理论性质。我们在一些最常见的拒绝推理方法的一般缺失数据设置中形式化了这些隐藏的假设。它揭示了隐藏的建模大多是不完整的，因此禁止在一般模型选择机制中比较现有方法（通过资助“不可资助”的申请人除外）。因此，我们在模拟数据和真实数据（来自欧洲主要贷款发行机构 CACF）上评估了这些方法的性能。不出所料，没有一种方法似乎是一致的。这些理论和实证结果不仅强化了谨慎使用经典拒绝推理方法的想法，而且还投资于未来的研究工作以设计基于模型的拒绝推理方法（不资助“不可资助”的申请人）。