  We study the problem of estimating a functional or a parameter in the context
where outcome is subject to nonignorable missingness. We completely avoid
modeling the regression relation, while allowing the propensity to be modeled
by a semiparametric logistic relation where the dependence on covariates is
unspecified. We discover a surprising phenomenon in that the estimation of the
parameter in the propensity model as well as the functional estimation can be
carried out without assessing the missingness dependence on covariates. This
allows us to propose a general class of estimators for both model parameter
estimation and functional estimation, including estimating the outcome mean.
The robustness of the estimators are nonstandard and are established rigorously
through theoretical derivations, and are supported by simulations and a data
application.
