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Abstract: We study semiparametric efficiency bounds and efficient estimation ofparameters defined through general moment restrictions with missing data.Identification relies on auxiliary data containing information about thedistribution of the missing variables conditional on proxy variables that areobserved in both the primary and the auxiliary database, when such distributionis common to the two data sets. The auxiliary sample can be independent of theprimary sample, or can be a subset of it. For both cases, we derive bounds whenthe probability of missing data given the proxy variables is unknown, or known,or belongs to a correctly specified parametric family. We find that theconditional probability is not ancillary when the two samples are independent.For all cases, we discuss efficient semiparametric estimators. An estimatorbased on a conditional expectation projection is shown to require milderregularity conditions than one based on inverse probability weighting.



Author: Xiaohong Chen, Han Hong, Alessandro Tarozzi

Source: https://arxiv.org/







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