Nonparametric functional data classification and bandwidth selection in the presence of MNAR class variables

The problem of nonparametric functional data classification and bandwidth selection is considered when the response variable, also called the class label, might be missing but not at random (MNAR). This setup is broadly acknowledged to be more challenging than the simpler case of missing at random setup. With the focus on kernel methods, we develop nonparametric classification rules and also propose bandwidth selection procedures for the proposed estimators. To study the performance of the resulting classifiers, we look into the rates of convergence of the misclassification error of the proposed method to that of the theoretically optimal classifier. The final-sample performance of our classifiers is assessed via numerical studies.