Annals of Statistics

Asymptotic Properties of the Balanced Repeated Replication Method for Sample Quantiles

Jun Shao and C. F. J. Wu

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Abstract

Inference, including variance estimation, can be made from stratified samples by selecting a balanced set of subsamples. This balanced subsampling method is generically called the balanced repeated replication method in survey data analysis, which includes McCarthy's balanced half-samples method and its extensions for more general stratified designs. We establish the asymptotic consistency of the balanced repeated replication variance estimators when the parameter of interest is the population quantile. The consistency results also hold when balanced subsampling is replaced by random subsampling. As a key technical prerequisite, we prove a Bahadur-type representation for sample quantiles in stratified random sampling.

Article information

Source
Ann. Statist., Volume 20, Number 3 (1992), 1571-1593.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348785

Digital Object Identifier
doi:10.1214/aos/1176348785

Mathematical Reviews number (MathSciNet)
MR1186266

Zentralblatt MATH identifier
0766.62005

JSTOR
links.jstor.org

Subjects
Primary: 62D05: Sampling theory, sample surveys
Secondary: 62G05: Estimation 62G99: None of the above, but in this section

Keywords
Bahadur representation balanced half-samples balanced subsampling random subsampling repeated random-group stratified samples

Citation

Shao, Jun; Wu, C. F. J. Asymptotic Properties of the Balanced Repeated Replication Method for Sample Quantiles. Ann. Statist. 20 (1992), no. 3, 1571--1593. doi:10.1214/aos/1176348785. https://projecteuclid.org/euclid.aos/1176348785


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