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A Direct Bootstrap Method for Complex Sampling Designs from a Finite Population
Résumé In complex designs, classical bootstrap methods result in a biased variance estimator when the sampling design is not taken into account. Resampled units are usually rescaled or weighted in order to achieve unbiasedness in the linear case. In the present article, we propose novel resampling methods that may be directly applied to variance estimation. These methods consist of selecting subsamples under a completely different sampling scheme from that which generated the original sample, which is composed of several sampling designs. In particular, a portion of the subsampled units is selected without replacement, while another is selected with replacement, thereby adjusting for the finite population setting. We show that these bootstrap estimators directly and precisely reproduce unbiased estimators of the variance in the linear case in a time-efficient manner, and eliminate the need for classical adjustment methods such as rescaling, correction factors, or artificial populations. Moreover, we show via simulation studies that our method is at least as efficient as those currently existing, which call for additional adjustment. This methodology can be applied to classical sampling designs, including simple random sampling with and without replacement, Poisson sampling, and unequal probability sampling with and without replacement.
   
Mots-clés
   
Citation Antal, E., & Tillé, Y. (2011). A Direct Bootstrap Method for Complex Sampling Designs from a Finite Population. Journal of the American Statistical Association, 106(494), 534-543.
   
Type Article de périodique (Anglais)
Date de publication 14-3-2011
Nom du périodique Journal of the American Statistical Association
Volume 106
Numéro 494
Pages 534-543
URL http://pubs.amstat.org/doi/abs/10.1198/jasa.2011.tm09767
Liée au projet Convention Université de Neuchâtel/Office fédéral de la s...