Quantile estimation with a complex survey design.(English)Zbl 0787.62011

A sequence $$\{\xi_ r\}$$ of stratified finite populations is considered, where the population in each stratum is a random sample of a finite number of clusters selected from an infinite superpopulation with a common distribution function $$F$$. It is assumed that a stratified random sample of clusters is selected without replacement from the population $$\xi_ r$$. The finite population distribution function $$F_{rN}$$ and its estimate $$F_{rn}$$ are considered (here $$N$$ and $$n$$ denote the number of clusters in the population and in the sample, respectively), and conditions under which $$F_{rn}$$ is asymptotically normal are established. Further, asymptotic properties of sample quantiles $$\hat q_{rn}(\gamma)=\inf\{x:F_{rn}(x)\geq\gamma\}$$ are studied and confidence intervals for population and superpopulation quantiles are constructed. The large-sample results are supported by a Monte Carlo study.

MSC:

 62D05 Sampling theory, sample surveys 62E20 Asymptotic distribution theory in statistics
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