A NEW ESTIMATION THEORY FOR SAMPLE SURVEYS.

A new estimation theory for sample surveys is proposed. The basic feature of the theory is a special parametrization of finite populations based on the assumption 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 unbiased minimum variance. 2 For simple random sampling with replacement, the sample mean based only on the distinct units in the sample is the maximum 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 a prior distribution is available, Bayes estimators can be derived using the complete likelihood. Author