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

Francisco, Carol A.; Fuller, Wayne A.

Ann. Stat. 19, No. 1, 454-469 (1991).

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

Keywords:

asymptotic normality; sequence of stratified finite populations; infinite superpopulation; stratified random sample of clusters; without replacement; finite population distribution function; asymptotic properties of sample quantiles; confidence intervals; superpopulation quantiles; large-sample results; Monte Carlo study