  Ordinal data are often seen in real applications. Regular multicategory
classification methods are not designed for this data type and a more proper
treatment is needed. We consider a framework of ordinal classification which
pools the results from binary classifiers together. An inherent difficulty of
this framework is that the class prediction can be ambiguous due to boundary
crossing. To fix this issue, we propose a noncrossing ordinal classification
method which materializes the framework by imposing noncrossing constraints. An
asymptotic study of the proposed method is conducted. We show by simulated and
data examples that the proposed method can improve the classification
performance for ordinal data without the ambiguity caused by boundary
crossings.
