The Finite Population Bootstrap - From the Maximum Likelihood to the Horvitz-Thompson Approach

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