Abstract: The main purpose of this study is to develop parameter identifiability and statistical inferences for a class of possibly over-identified nonsmooth moment functions with nonignorable missing data. Assuming a parametric model on the respondent probability, we propose a propensity score-based nonparametric imputation approach that uses an instrumental variable to address model identifiability in the presence of nonignorable missing data. A set of augmented inverse probability weighting moment functions is constructed as a basis for inferences performed using the generalized empirical likelihood method. Under some mild regularity conditions, we establish the large-sample properties of the resultant two-step generalized empirical likelihood estimators and generalized empirical likelihood ratio statistics for the case in which the propensity score is estimated parametrically using a correctly specified model. A derivative-free optimization method based on the simulated annealing algorithm is developed to implement the proposed methods. The methods are illustrated using simulations and an application to a data set on the serum-cholesterol levels of heart-attack patients.

Key words and phrases: Generalized empirical likelihood, identification, instrumental variable, nonignorable missing data, nonsmooth moment conditions, simulated annealing algorithm.