Generalized framework for defining the optimal inclusion probabilities of one-stage sampling designs for multivariate and multi-domain surveys

Piero Demetrio Falorsi and Paolo RighiNote 1

Abstract

This paper introduces a general framework for deriving the optimal inclusion probabilities for a variety of survey contexts in which disseminating survey estimates of pre-established accuracy for a multiplicity of both variables and domains of interest is required. The framework can define either standard stratified or incomplete stratified sampling designs. The optimal inclusion probabilities are obtained by minimizing costs through an algorithm that guarantees the bounding of sampling errors at the domains level, assuming that the domain membership variables are available in the sampling frame. The target variables are unknown, but can be predicted with suitable super-population models. The algorithm takes properly into account this model uncertainty. Some experiments based on real data show the empirical properties of the algorithm.

Key Words: Optimal Allocation; Multi-way stratification; Domain estimates; Balanced Sampling.

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