Kernel Density Estimation with Missing Data: Misspecifying the Missing Data Mechanism

This paper explores additional properties of an inverse propensity score weighted kernel density estimator for estimating the density of incomplete data. This estimator is based on the Horvitz-Thompson estimator and requires estimating the propensity score assuming the response variable is missing at random. Nonparametric methods are used to estimate the propensity scores. Implications of misspecifying the missing data mechanism on the performance of the density estimator are discussed and evaluated. In addition, an augmented inverse propensity score weighted kernel density estimator, which is not influenced by this misspecification, is proposed and evaluated.