Online Program

Optimal Allocation for Multidomain, Multivariate Case with different amount of auxiliary information
*Piero Demetrio Falorsi, Italian NSI, ISTAT 
Paolo Righi, Italian NSI, ISTAT 

Keywords: Sampling allocation, incomplete stratification, business surveys

Commonly, the business surveys produce estimates for a huge number of domains that define two or more partitions of the target population. When domain indicator variables are known at population level then a multi-way (or incomplete) stratification design can be used, guaranteeing a sample with planned size in each domain. The multi-way approach has some advantages with respect to the standard approach (using a one-way stratified design where the strata are obtained combining the domains of the partitions) such as: the sample allocation is more efficient (smaller sample size with same sampling errors); the response burden is reduced both in a given survey occasion and considering several survey occasions (for the combining strata with small population sizes the one-way design selects with high probability or sometime with certainty some business units in each survey occasion producing a great statistical burden). The paper shows an algorithm for defining an optimal sample allocation for the multi-way design according to the definition proposed by Bethel (1989). The procedure is suitable in the multivariate-multidomain case and assumes that the multi-way random sample selection is performed by the cube algorithm (Deville and Tillé, 2004). Furthermore, the paper considers the case where the sampling frame may be partitioned according to the different number of auxiliary variables (deriving from several administrative and statistical sources) available for each unit.