Criticalities in applying the Neyman\u2019s optimality in business surveys : a comparison of selected allocation methods

In finite population sampling, when dealing with negligible sampling fractions (budget constraints) or when data quality is not satisfactory (e.g. frame lists, auxiliary information, etc.), a rethinking of Tchuprow\u2019s (1924) optimality concept (later extended by Neyman, 1934) in stratified sampling is needed. In fact, the need of stratum representativeness from one side and the optimum allocation from the other are often in conflict. Furthermore, the choice of a sampling design which is rigorously respectful of the statistical theory is a difficult task in practice, especially when knowledge barriers and operational constraints are present. Sometimes a purposive design is the only possibility. This work aims at finding an optimal allocation method from a population of enterprises. This task is carried out through a simulation approach which compares different methodologies. We consider, among others, and together with the popular optimal allocation and its multivariate extension (Bethel\u2019s algorithm -1989), the \u2018Optimum Robust Allocation with Uniform Stratum Threshold \u2013 AORSU\u2019 (Chiodini P.M., Manzi G., Verrecchia F.; 2008) and the \u2018dynamic allocation\u2019 (Buisson, 2009). These methods are suitable both for domain analyses and for the improvement of the estimates, obtained through a proxy of the stratum variability. In general, AORSU is useful when an ex-ante allocation is possible. On the other hand the dynamic allocation (i.e. ex-post) is becoming more and more of interest especially when no information about stratum variability is available. The method relies on an in itinere adjustment process (i.e. an allocation based upon an estimate of the sampling variance of the first sampling data from the strata). For the latter method, even though a number of practical solutions for the survey list are available (see, e.g., Chiodini P.M., Facchinetti, Manzi G., Nai Ruscone M., Verrecchia F, 2008), the substitution of sampling units to be interviewed, which is routinely performed, is the real practical drawback, especially when organizational problems, related to target shifting, arise. The solution to this is generally not trivial. Simulations will be carried out on different databases (ASIA - ISTAT; Italian Register of enterprises - Chamber of Commerce of Milan, Italy