Each week, we publish layman’s abstracts of new articles from our prestigious portfolio of journals in statistics. The aim is to highlight the latest research to a broader audience in an accessible format.
Regression function estimation is a classical problem in statistics, with wide applications in many scientific fields. This paper considered regression estimation when there is a potential selection-biased sampling (i.e., the sample obtained is not representative of the population intended to be analyzed) or missing data in predictors. In particular, the authors propose a new method to estimate the 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 (MAR).
Besides the desirable asymptotic normality result with a root-n convergence rate, the proposed regression estimate has several appealing features. First, with predictors MAR, the proposed approach does not need to specify the missing probability function or the predictors’ distribution in contrast to existing methods. Second, the new method utilizes all the available information. Finally, the baseline distribution of the response is unspecified. These features demonstrate the flexibility and robustness of the proposed method. This work will be interesting to not only statisticians working on methodology development but also practitioners in various fields.