Abstract: We address the problem of imputation when a response or covariate may be subject to a nonignorable (or, equivalently, missing not at random) nonresponse, meaning the response probability may depend on a variable that is not always observed. We discuss model identification and develop a novel estimator of the parameters of the response probability. We use a propensity score adjustment to incorporate a subset for which both the response and the covariate are missing. We derive an approximation for the large-sample variance and assess the finite-sample properties of the variance estimator using simulations. The simulation results also show that a quantile regression offers a compromise between fully parametric and nonparametric alternatives. In an application to data from a 2011 survey of pet owners, a quantile regression allows us to model complex relations between two types of veterinary expenditures, where we find evidence of a nonignorable onresponse.

Key words and phrases: B-spline, missing not at random, survey sampling.