Simple Robust Estimating Method for Generalized Linear Models and its Application to Propensity Score Estimation

A generalized linear model is one of the most well-known model families in statistics. Of course, we should specify the correct model structure to estimate the unbiased result and make a valid inference, however, we would like to consider an another rational approach in this paper to make a valid inference. The proposed method is 1) preparing some candidate models, and 2) construct an estimating equation including the candidate models at once (do not have to select just one) to estimate an interested parameter. If the correct model was included in the candidate models, the parameter estimator would have the consistency. By using the idea, we will consider a robust estimating method to estimate a "valid" parameter estimator without any model/variable selection methods. As an application example, an estimation of a propensity score and a generalized propensity score will be considered.