It is known that informative sampling and nonignorable nonresponse mechanism bias standard estimators of population parameters characterized superpoulation model and predictors of finite population total. This paper introduces new estimators of superpoulation population model parameters and new predictors of finite population total. The proposed estimators and predictors account for the joint effects of informative sampling designs and of not missing at random nonresponse mechanism in statistical models for complex survey data. For this purpose, theoretically, we use the response distribution and relationships between moments of the superpopoulation, sample, sample-complement, response, and non-response distributions, for the prediction of finite population totals. The derived parametric best linear unbiased predictors of finite population total, use the observation for response set of the study variable or variable of interest, values of auxiliary variables and their population totals, sampling weights, and propensity scores. An interesting outcome of the present study is that most predictors known from model-based survey sampling, can be derived as a special case from this general theory.

 

Keywords: Response Distribution, Nonignorable Nonresponse, Informative Sampling Design.