Bootstrap inference for the finite population total under complex sampling designs

Date
2019-01-07
Authors
Wang, Zhonglei
Kim, Jae Kwang
Kim, Jae Kwang
Peng, Liuhua
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Altmetrics
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Statistics
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Statistics
Abstract

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

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This pre-print is made available through arxiv: https://arxiv.org/abs/1901.01645.

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