Kernel regression estimation for incomplete data with applications

Methods are proposed to construct kernel estimators of a regression function in the presence of incomplete data. Furthermore, exponential upper bounds are derived on the performance of the L_p norms of the proposed estimators, which can then be used to establish various strong convergence results. The presence of incomplete data points are handled by a Horvitz–Thompson-type inverse weighting approach, where the unknown selection probabilities are estimated by both kernel regression and least-squares methods. As an immediate application of these results, the problem of nonparametric classification with partially observed data will be studied.