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Biometrika 2004 91(4):893-912; doi:10.1093/biomet/91.4.893
© 2004 by Biometrika Trust
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Efficient balanced sampling: The cube method

Jean-Claude Deville1 and Yves Tillé2

1 Laboratoire de Statistique d'Enquête, CREST-ENSAI, École Nationale de la Statistique et de l'Analyse de l'Information, rue Blaise Pascal, Campus de Ker Lann, 35170 Bruz, France deville{at}ensai.fr, 2 Groupe de Statistique, Université de Neuchâtel, Espace de l'Europe 4, Case postale 805, 2002 Neuchâtel, Switzerland yves.tille{at}unine.ch

A balanced sampling design is defined by the property that the Horvitz–Thompson estimators of the population totals of a set of auxiliary variables equal the known totals of these variables. Therefore the variances of estimators of totals of all the variables of interest are reduced, depending on the correlations of these variables with the controlled variables. In this paper, we develop a general method, called the cube method, for selecting approximately balanced samples with equal or unequal inclusion probabilities and any number of auxiliary variables.

Key Words: Calibration; Poststratification; Quota sampling; Sampling algorithm; Stratification; Sunter's method; Unequal selection probabilities

Received September 2002. Revised March 2004.


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