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Primary Submission Category: Missing data

Missing not at random: a cross-sectional model

Authors: Anna Guo, Razieh Nabi, Jiwei Zhao,

Presenting Author: Anna Guo*

Conducting valid statistical inference is challenging in the presence of nonignorable missing mechanisms, often referred to as missing-not-at-random or MNAR for short. In this work, we consider a MNAR missingness mechanism, most appropriate in cross-sectional studies. This model is a supermodel of several popular models, including permutation model (Robins 1997), block-conditional MAR model (Zhou et al. 2010), and block-parallel model (Mohan et al. 2013), thus making it less stringent in terms of underlying statistical assumptions. The underlying complete-data distribution in our cross-sectional MNAR model is not nonparametrically identifiable from the partially observed data. We establish sufficient conditions for identification of the target law by restricting our attention to the exponential family distributions. Unlike most prior work, all variables in our model can be subject to missingness, i.e., our results do not rely on the presence of fully observed variables. Borrowing the graphical model toolkit, we propose methods for testing the independence restrictions encoded in our model. If the test result suggests further independence restrictions in the model, we show that the model is nonparametrically identifiable. We also adopt a conditional likelihood approach for independence tests via estimating pairwise odds ratios. Further, we suggest the generalized method of moments for target law estimation. Statistical properties of the estimators are established.