The Finite Population Bootstrap - From the Maximum Likelihood to the Horvitz-Thompson Approach
The finite population bootstrap method is used as a computer-
intensive alternative to estimate the sampling distribution of a sample statis-
tic. The generation of a so-called “bootstrap population” is the necessary
step between the original sample drawn and the resamples needed to mimic
this distribution. The most important question for researchers to answer is
how to create an adequate bootstrap population, which may serve as a close-
to-reality basis for the resampling process. In this paper, a review of some
approaches to answer this fundamental question is presented. Moreover, an
approach based on the idea behind the Horvitz-Thompson estimator allow-
ing not only whole units in the bootstrap population but also parts of whole
units is proposed. In a simulation study, this method is compared with a more
heuristic technique from the bootstrap literature.
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