On the Maximum Likelihood Estimation of Population and Domain Means

Estimating of population and domain means based on model-design approaches is considered in this paper. Population elements randomly belong to domains. A joint distribution of the variable under study and an auxiliary variable is assumed. Data are observed in a sample selected from a fixed population. The partition of the sample elements into domains of the population is also known. Outside of the sample, values of the auxiliary variable are known but their partition among the domains is not known. The domain means are estimated based on the likelihood function of the data observed in the sample and outside of it. The maximum likelihood estimation method provides regression-type estimators of domain means of the variable under study. They are dependent on posterior probabilities that observations of the auxiliary variable belong to particular domains. Moreover, the weighted means of the domain averages estimators are used to estimation of the population mean. The accuracy of the evaluated estimators and the ordinary estimator is compared using a simulation analysis. The results of this paper could be useful in economic, demographic and sociological surveys.