Sample selection when a multivariate set of size measures is available

摘要

The design of a ps random sample from a finite population when multivariate auxiliary variables are available deals with two main issues: the definition of a selection probability for each unit in the population as a function of the whole set of the auxiliary variables and the determination of the sample size required to achieve a fixed precision level for each auxiliary variable. These precisions are usually expressed as a set of upper limits on the coefficients of variation of the estimates. A strategy, based on a convex linear combination of the univariate selection probabilities, is suggested to approach jointly these issues. The weights of the linear combination are evaluated in such a way that the sample sizes necessary to reach each constrained error level are the same. The procedure is applied to design a ps sampling scheme for the monthly slaughtering survey conducted by the Italian Institute of Statistics (Istat). The results clearly show that the use of this strategy implies an appreciable gain in the efficiency of the design. The selection probabilities returned by this proposal do not involve excessive and unnecessary efforts on some auxiliary variables, disadvantaging other variables that for this reason will have too high errors. On the contrary, this may occur when simple summary statistics are used (average, maximum, etc.) to reduce the multivariate problem to a known univariate situation. For a given set of precision levels, our procedure achieves a sample size which is much lower than the one used by Istat and obtained through a multivariate stratification of the frame.