Bootstrap Inference with Stratified Samples.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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Most sample surveys involve stratification and multi-stage clustered sampling. A recent trend in survey data analysis is inference about nonlinear statistics from complex samples. Available methods include the linearization, jackknife and balanced half-samples. In the non-survey context, another method called the bootstrap has been shown to enjoy other desirable properties, the most important one being that it reflects the skewness inherent in the original point estimate. It is shown that a straightforward extension of the usual bootstrap provides incorrect variance estimates and misleading confidence intervals. A correct version is constructed by adjusting for a scaling problem before applying the nonlinear transformation. Several desirable theoretical properties of the proposed method are described. A detailed study in the special case of the combined ratio estimator is given. Author
- Statistics and Probability