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We study the problem of estimating a functional or a parameter in the contextwhere outcome is subject to nonignorable missingness. We completely avoidmodeling the regression relation, while allowing the propensity to be modeledby a semiparametric logistic relation where the dependence on covariates isunspecified. We discover a surprising phenomenon in that the estimation of theparameter in the propensity model as well as the functional estimation can becarried out without assessing the missingness dependence on covariates. Thisallows us to propose a general class of estimators for both model parameterestimation and functional estimation, including estimating the outcome mean.The robustness of the estimators are nonstandard and are established rigorouslythrough theoretical derivations, and are supported by simulations and a dataapplication.

Avoid Estimating the Unknown Function in a Semiparametric Nonignorable Propensity Model