On classification with incomplete covariates

摘要

Procedures are proposed to perform classification when a covariate vector may have missing values. The proposed methods use a combination of least-squares and kernel imputation to construct a classifier. The associated function-indexed empirical processes provide the right theoretical tool to assess the performance of the resulting classifiers. This is done by obtaining exponential bounds on the probability of the deviations of the conditional errors of the constructed classifier from that of the best (optimal) classifier. Such bounds, in conjunction with the Borel-Cantelli lemma, yield various strong consistency results.