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Abstract:
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We consider sequential problems with missing covariates and partially observed responses. When there are missing covariates, constructing estimators for the desired parameter of interest can be difficult. We introduce a process for constructing a multistage estimator that can exhibit a multiply robustness property. Three classical problems from the statistics literature are discussed: the Cox model from survival analysis, missing response, and binary treatment from causal inference. Furthermore, when covariates can take on an arbitrary missing pattern, nonparametric identification of the full-data distribution is not straightforward because the classical assumptions may no longer be sufficient. For theoretical interest, we discuss an enhanced identification theory where we generalize the classical assumptions to ones that are compatible with existing problem-specific assumptions that assume fully-observed covariates.
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