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

Abstract

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 necessarystep between the original sample drawn and the resamples needed to mimicthis distribution. The most important question for researchers to answer ishow 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 someapproaches to answer this fundamental question is presented. Moreover, anapproach based on the idea behind the Horvitz-Thompson estimator allow-ing not only whole units in the bootstrap population but also parts of wholeunits is proposed. In a simulation study, this method is compared with a moreheuristic technique from the bootstrap literature.