| Content | Bootstrap is a useful computational tool for statistical inference, but it may lead to erroneous analysis under complex survey sampling. In this paper, we propose a unified bootstrap method for stratified multi-stage cluster sampling, Poisson sampling, simple random sampling without replacement and probability proportional to size sampling with replacement. In the proposed bootstrap method, we first generate bootstrap finite populations, apply the same sampling design to each bootstrap population to get a bootstrap sample, and then apply studentization. The second-order accuracy of the proposed bootstrap method is established by the Edgeworth expansion. Simulation studies confirm that the proposed bootstrap method outperforms the commonly used Wald-type method in terms of coverage, especially when the sample size is not large. |
