A new estimator and approach for estimating the subpopulation parameters

Based on some theoretical results, we recommend a new algorithm for estimating the total and mean of a subpopulation variable for the case of a known subpopulation size, which is different from the algorithm recommended by most of sampling books. The latter usually recommend the multiplication of the subpopulation sample mean by the subpopulation size rather than the subpopulation total estimator for the unknown subpopulation size. We present a criterion to determine which estimator is more efficient. The criterion shows that the traditional total subpopulation estimator for unknown subpopulation size will be more efficient if the subpopulation mean is close to zero. Using an innovative procedure, we develop a new estimator, and we study its properties using real data. The new estimator is potentially an appropriate direct estimator in a composite estimator for small area estimation.