Annals of Statistics

Asymptotic Properties of the Balanced Repeated Replication Method for Sample Quantiles

Jun Shao and C. F. J. Wu

Full-text: Open access


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

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

First available in Project Euclid: 12 April 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


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

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


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.

Export citation