New semiparametric regression method with applications in selection-biased sampling and missing data problems

We propose a new method to estimate a regression function based on the semiparametric density ratio model, which can be viewed as a generalized linear model with a canonical link function and an unspecified baseline distribution function. Under this model, the distribution of the observed data retains the same structure in the presence of selection-biased sampling or when the predictors are missing at random. In particular, in the latter case, the new method utilizes all the available information and does not need to specify the distribution of the predictors or the probability of observing the predictors. We establish large sample properties of the proposed regression estimators. Simulation studies demonstrate that the proposed estimators perform well in practical situations. Empirical data from the National Health and Nutrition Examination Survey are presented.