A new estimation theory for sample surveys

A new estimation theory for sample surveys is proposed, the basic feature of which is a special parametrization of finite populations based on the assumptions that a character attached to the units is measured on a known scale with a finite set of scale points. In the class of estimators which do not functionally depend on the identification labels preattached to the units, the following results are proved: (1) For simple or stratified simple random sampling without replacement, the customary estimators are minimum variance unbiased. (2) For simple random sampling with replacement, the sample mean based only on the distinct units in the sample is the maximurn-likelihood estimator of the population mean. (3) If a concomitant variable with known population mean is also observed, an approximation to the maximum-likelihood estimator of the population mean is closely related to the customary regression estimator. (4) If prior information in the form of a prior distribution is available, Bayes estimators can be derived using the complete likelihood.