  Real-world classifiers can benefit from the option of abstaining from
predicting on samples where they have low confidence. Such abstention is
particularly useful on samples which are close to the learned decision
boundary, or which are outliers with respect to the training sample. These
settings have been the subject of extensive but disjoint study in the selective
classification (SC) and out-of-distribution (OOD) detection literature. Recent
work on selective classification with OOD detection (SCOD) has argued for the
unified study of these problems; however, the formal underpinnings of this
problem are still nascent, and existing techniques are heuristic in nature. In
this paper, we propose new plugin estimators for SCOD that are theoretically
grounded, effective, and generalise existing approaches from the SC and OOD
detection literature. In the course of our analysis, we formally explicate how
na\"{i}ve use of existing SC and OOD detection baselines may be inadequate for
SCOD. We empirically demonstrate that our approaches yields competitive SC and
OOD detection performance compared to baselines from both literatures.
