Confronti fra stimatori per la media nel campionamento per centri

The center sampling technique is well suited when a population is naturally gathered in overlapping groups of units for which the units can not be labeled and the group size as well as the population size are unknown. An unbiased estimator Ym for the mean of a quantitative characteristic of interest has been proposed under the simple hypotheses that the relative weight of each center is known. A second estimator Yc can be deduced from a previous proposal under the same hypothesis. In the present paper the exact variance of Yc together with an estimate of it are given. The two estimators are based on different ways of summarizing data and they coincide in the case of proportional allocation of the overall sample size only. A comparison between the two estimators is accomplished both from the inferential and from the practical point of view. Through a simulation study it is shown that no estimator is uniformly more efficient than the other in the general case of L>_2 centers. Besides it comes out that Yc is more efficient when there is a "small" variability of the center sampling fractions, while Ym is more efficient as this variability increases. Simulation also shows that the proposed estimators for the variance are asymptotically unbiased, consistent and c-consistent