On histogram-based regression and classification with incomplete data

Abstract

We consider the problem of nonparametric regression with possibly incomplete covariate vectors. The proposed estimators, which are based on histogram methods, are fully nonparametric and straightforward to implement. The presence of incomplete covariates is handled by an inverse weighting method, where the weights are estimates of the conditional probabilities of having incomplete covariate vectors. We also derive various exponential bounds on the L 1 norms of our estimators, which can be used to establish strong consistency results for the corresponding, closely related, problem of nonparametric classification with missing covariates. As the main focus and application of our results, we consider the problem of pattern recognition and statistical classification in the presence of incomplete covariates and propose histogram classifiers that are asymptotically optimal.