Optimal estimates and optimal predictors of finite population characteristics in the presence of nonresponse

Summary

When samples from a finite population are studied, for instance by interview, there will usually be some units from which no response is obtained. In this paper optimal predictors of finite population characteristics, when nonresponse is present, are studied. The predictors are studied under simple regression superpopulation models. The optimal predictors are connected to the classical weighted sample estimates which are shown to be maximum likelihood estimates, provided the probability function is fully described by the sampling design. The predictors are compared with respects to their efficiencies for some simple models and a possible explanation to the fact that the poststratification estimate which compensate for nonresponse does no better than the simple estimate, is pointed out.