On product estimation in simple random sampling

Abstract

The variance and the mean square error of the biased product stimator, as well as the variance of the unbiased estimator, are computed in terms of population moments in sampling both with and without replacement. It is shown that the preferability of one or the other estimator depends on the population. Unbiased sub-optimal estimators of the variances and the mean square errors are computed in terms of sample moments. On the basis of these results, a data-adaptive estimator is proposed. Questions relative to transformations of the auxiliary variate and to multivariate product estimation are also discussed.