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Unequal probability sampling without replacement through a splitting method

Jean-Claude Deville & Yves Tillé

Résumé A very general class of sampling methods without replacement and with unequal probabilities is proposed. It consists of splitting the inclusion probability vector into several new inclusion probability vectors. One of these vectors is chosen randomly; thus, the initial problem is reduced to another sampling problem with unequal probabilities. This splitting is then repeated on these new vectors of inclusion probabilities; at each step, the sampling problem is reduced to a simpler problem. The simplicity of this technique allows one to generate easily new sampling procedures with unequal probabilities. The splitting method also generalises well-known methods such as the Midzuno method, the elimination procedure and the Chao procedure. Next, a sufficient condition is given in order that a splitting method satisfies the Sen-Yates-Grundy condition. Finally, it is shown that the elimination procedure satisfies the Gabler sufficient condition.
   
Mots-clés Sampling without replacement Unequal probability sampling
   
Citation Deville, J. C., & Tillé, Y. (1998). Unequal probability sampling without replacement through a splitting method. Biometrika, 85(1), 89-101.
   
Type Article de périodique (Anglais)
Date de publication 24-3-1998
Nom du périodique Biometrika
Volume 85
Numéro 1
Pages 89-101
URL http://biomet.oxfordjournals.org/content/85/1/89.abstract