A unified asymptotic statistical theory is developed for making reliable statistical inferences for a large class of possibly misspecified regression models (e.g., linear, nonlinear, and categorical regression) with ignorable missing data mechanisms. The theory also handles misspecification of the missing data mechanism so that asymptotic inferences are reliable for nonignorable response data (i.e., Missing Not At Random or MNAR) statistical environments. In this talk, we present the key theorems of this new asymptotic theory for the special case of discrete random variables. Specifically, these new theorems establish asymptotic parameter estimate consistency and normality in the presence of model misspecification within MNAR statistical environments. In addition, explicit regularity conditions for the Orchard and Woodbury (1972; also see Louis, 1982) Missing Information Principle are provided which are directly relevant to possibly misspecified models within MNAR environments. The theory is directly applicable to a wide variety of modeling situations including problems dealing with verification and "work up" bias, parameter estimation and inference in Hidden Markov Models, random effects regression models, Item Response Theory, and missing data in surveys where question-content influences patterns of missingness. |