Two-step centre sampling for estimating the size, total and mean of elusive population

Abstract.

The estimation of the size of an elusive population is a frequently addressed problem in many fields of applications. The paper proposes a two step sampling strategy for the estimation of the population size, under the assumption that each unit of the population is present at least in one centre of aggregation. In the first step a sample of centres is selected and in the second step, from the selected centres, a sample of ultimate units is observed. The design extends the traditional network sampling introducing an additional step of selection. The properties of the Horvitz-Thompson type estimator are evaluated in a design-based approach: the estimator is admissible and consistent; the design is measurable. The approach is also used to estimate other descriptive parameters (the total and the mean of a study variable) for the same population. The expressions of the variance of all the proposed estimators and of their unbiased sample estimators are also proposed. The strategy is applied to a simulated population.