Criticalities in Applying the Neyman’s Optimality in Business Surveys: a Comparison of Selected Allocation Methods

In finite population sampling, when dealing with negligible sampling fractions (due, for example, to budget restrictions), or when stratification criteria definitions are not statistical in nature (e.g. heterogeneous administrative settings), or when data quality is not satisfactory (for example, when frame lists are out of date, or auxiliary information is required), a rethinking of Tschuprow’s (1924) optimality concept (later extended by Neyman, 1934) in stratified sampling is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 that rigorously obeys to the laws of standard 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 the most suitable allocation method for a finite population of enterprises by taking into account the above-mentioned restrictions, and is carried out through a simulation approach which compares different methodologies. We consider, among others and together with the popular optimal allocation method, the ISAE (Institute for Studies and Economic Analysis) methodology (Martelli, 1998; Malgarini, Margani, and Martelli, 2005) and the Optimum Robust Allocation with Uniform Stratum Threshold (AORSU) method (Chiodini, Manzi, and Verrecchia, 2008). These methods fit both with domain analyses and in relation to the improvement of the estimates which are obtained through a proxy of the stratum variability. In general, the methods considered are useful when an ex-ante allocation is possible. Simulation studies are carried out on the ASIA – ISTAT database (the Italian Register of enterprises).