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Bootstrap is a useful tool for making statistical inference, but it mayprovide erroneous results under complex survey sampling. Most studies aboutbootstrap-based inference are developed under simple random sampling andstratified random sampling. In this paper, we propose a unified bootstrapmethod applicable to some complex sampling designs, including Poisson samplingand probability-proportional-to-size sampling. Two main features of theproposed bootstrap method are that studentization is used to make inference,and the finite population is bootstrapped based on a multinomial distributionby incorporating the sampling information. We show that the proposed bootstrapmethod is second-order accurate using the Edgeworth expansion. Two simulationstudies are conducted to compare the proposed bootstrap method with theWald-type method, which is widely used in survey sampling. Results show thatthe proposed bootstrap method is better in terms of coverage rate especiallywhen sample size is limited.

Bootstrap inference for the finite population total under complex sampling designs