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WITHDRAWN - A General Algorithm for Multivariate Stratification
*Roberto Benedetti, ISTAT 
Federica Piersimoni, Istat 

Keywords: optimal stratification, combinatorial optimization, simulated annealing

The design of a stratified simple random sample without replacement from a finite population deals with two main issues: the definition of a rule to partition the population into strata, and the allocation of sampling units in the selected strata. This paper examines a stochastic relaxation strategy which plans to approach jointly these issues when the survey is multipurpose and multivariate quantitative information is available. Due to the multivariate nature of the model, we employ the theory of stochastic relaxation and use the simulated annealing algorithm. Strata are formed through a random search algorithm that, for a fixed number of strata, assign each record of the frame to the strata that minimize at each step, the sample allocation required to achieve the precision levels set for each surveyed variable. In this way, large numbers of constraints can be satisfied without drastically increasing the sample size, and also without discarding variables selected for stratification. Furthermore, the algorithm tends not to define empty or almost empty strata, thus avoiding the need for strata collapsing aggregations. The procedure was applied to redesign the italian survey on slaughtering firms. The results indicate that the gain in efficiency held using our strategy is nontrivial.