Kernel classification with missing data and the choice of smoothing parameters

Methods are proposed for selecting smoothing parameters of kernel classifiers in the presence of missing covariates. Here the missing covariates can appear in both the data and in the unclassified observation that has to be classified. The proposed methods are quite straightforward to implement. Exponential performance bounds will be derived for the resulting classifiers. Such bounds, in conjunction with the Borel–Cantelli lemma, provide various strong consistency results. Several numerical examples are presented to illustrate the effectiveness of the proposed procedures.