Product estimators in sample surveys

In the theory of sampling from finite populations, the well known concept of "ratio estimator" is an extremely useful and widely used device. This dissertation is concerned with developing an analogous concept in the form of a "product estimator" constituting as it were the product of two or more random variables X.Y.Z. More specifically this dissertation covers the development of formulas for expectations and variances of products of two and three factors in both, samples from finite and infinite populations. The so-called k-statistics, computed from simple random samples, are then employed for the estimation of the components of the variance formulas. The concept of an "unbiased product estimator" is introduced and exact variance formulas derived. An application of the concepts developed to a problem in crop estimation is illustrated by data supplied by the statistical Reporting Service (U.S.D.A.)