Bootstrap pour un tirage à plusieurs degrés avec échantillonnage à forte entropie à chaque degré

In this paper we propose a Bootstrap technique for multistage sampling with large entropy samplingdesigns at each stage. Our method enables easy variance estimates for both linear and non linearstatistics. It consists in a correction of the method originally proposed by Gross (1980) for simplerandom sampling, and known not to be consistent for multistage sampling. The idea consists in buildinga pseudo-population of pseudo Primary Sampling Units, based on the original sample. The first stagedrawing is performed, but the second stage drawing is corrected to get the usual variance estimate in thelinear case. Two stage sampling with simple random sampling at each stage and self-weighted two stagesampling are covered by the proposed Bootstrap technique. The method is evaluated through a limitedset of simulations.