Kernel regression estimation for incomplete data with applications

Abstract

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.

Kernel classification with missing data and the choice of smoothing parameters

“…The idea of replacing the unknown regression functions with their kernel regression estimates is fairly common in the literature on regression function estimation with missing data. For example, Mojirsheibani and Reese (2015) prove the strong consistency of such kernel regression estimates when the response variables can be missing; see also Karimi and Mohammadzadeh (2012) and Toutenburg and Shalabh (2003) for more on the estimation of regression functions for correlated data in the presence of missing response variables.…”