Some results on classifier selection with missing covariates

Methods are proposed to choose classifiers from a given collection of classifiers when there are missing covariates in the data. Two situations are considered: (i) the case where the new observation (to be classified) has no missing covariates and (ii) the case where the new observation is also allowed to have missing covariates. Using arguments from the empirical process theory, exponential performance bounds will be derived for the resulting classifiers. Such bounds, together with the Borel-Cantelli lemma, yield various strong consistency results.