Nonparametric and semiparametric regression with missing data

In this dissertation, we consider nonparametric and semiparametric regression for both independent and longitudinal data with missing at random (MAR). The thesis consists of three chapters. In chapter 1, we focus on nonparametric regression of a scalar outcome on a covariate when the outcome is MAR. We show that the usual nonparametric kernel regression estimation based only on complete cases is generally inconsistent. We propose inverse probability weighted (IPW) kernel estimating equations (KEEs) and a class of augmented IPW (AIPW) KEEs. Both approaches do not require specification of a parametric model for the error distribution. We show that the IPW kernel estimator is consistent when the probability that a sampling unit is observed, i.e., the selection probability, is known by design or is estimated using a correctly specified model. We further show that the AIPW kernel estimator is double-robust in the sense that it is consistent if either the model for the selection probability or the model for the conditional mean of the outcome given covariates and auxiliary variables is correctly specified, not necessarily both. We argue that adequate augmentation terms in the AIPW KEEs h