A Unified Approach for Defining Optimal Multivariate and Multi-Domains Sampling Designs

Abstract

The present paper illustrates a sampling method based on balanced sampling, practical and easy to implement, which may represent a general and unified approach for defining the optimal inclusion probabilities and the related domain sampling sizes in many different survey contexts characterized by the need of disseminating survey estimates of prefixed accuracy for a multiplicity both of variables and of domains of interest. The method, depending on how it is parameterized, can define a standard cross-classified or a multi-way stratified design. The sampling algorithm defines an optimal solution—by minimizing either the costs or the sampling sizes—which guarantees: (1) lower sampling errors of the domain estimates than given thresholds and (2) that in each sampling selection the sampling sizes for all the domains of interest are fixed and equal to the planned ones. It is supposed that, at the moment of designing the sample strategy, the domain membership variables are known and available in the sampling frame and that the target variables are unknown but can be predicted with suitable superpopulation models.