A comparison between pivotal sampling and multinomial sampling

Abstract

When sampling in a finite population, an important step lies in the choice of inclusion probabilities for the sampling units and of a sampling algorithm respecting these probabilities. This algorithm needs to be efficient, i.e. makes use of available auxiliary information to draw samples leading to accurate estimators. Yet, no without replacement sampling algorithm is uniformly better in terms of accuracy; this led to numerous sampling algorithms, listed in Brewer and Hanif (1983), and Tillé (2006). The Cube method is a recent breakthrough, and enables the selection of balanced samples providing exact (or at least, very accurate) estimations for totals of auxiliary variables. The pivotal method (Deville and Tillé, 1998 ; Srinivasan, 2001) is an important particular case, obtained with the sole balancing constraint which leads to fixed-size sampling. In this work, we show that ordered pivotal sampling is always more efficient than multinomial sampling, for given 1st order moments. This result ensures that any randomized version of the pivotal method shares the same property of efficiency. This is joint work with Anne Ruiz-Gazen (Toulouse School of Economics). References Brewer, K.R.W., & Hanif, M. (1983). Sampling with unequal probabilities. Springer, New York, Berlin.