A comparison of pivotal sampling and unequal probability sampling with replacement

Guillaume Chauvet (1) , Anne Ruiz-Gazen (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We prove that any implementation of pivotal sampling is more efficient than multinomial sampling. This yields the weak consistency of the Horvitz Thompson estimator and the existence of a conservative variance estimator. A small simulation study supports our findings.

Mots clés: Cube method; Mean-square consistency; Sampling algorithm; unequal probabilities; Variance estimator; with-replacement sampling

Domaines: Statistiques [math.ST]

Guillaume Chauvet, Anne Ruiz-Gazen. A comparison of pivotal sampling and unequal probability sampling with replacement. Statistics and Probability Letters, 2017, 121, pp.1-5. ⟨10.1016/j.spl.2016.09.027⟩. ⟨hal-01464468⟩