A quantile estimator under two-phase sampling for stratification

Abstract

Recently, the estimation of a population quantile has received quite attention. Existing quantile estimators generally assume that values of an auxiliary variable are known for the entire population, and most of them are defined under simple random sampling without replacement. Assuming two-phase sampling for stratification with arbitrary sampling designs in each of the two phases, a new quantile estimator and its variance estimator are defined. The proposed estimators can be used when the population auxiliary information is not available, which is a common situation in practice. Desirable properties such as the unbiasedness are derived. Suggested estimators are compared numerically with an alternative stratification estimator and its variance estimator, and desirable results are observed. Confidence intervals based upon the proposed estimators are also defined, and they are compared via simulation studies with the confidence intervals based upon the stratification estimator. The proposed confidence intervals give desirable coverage probabilities with the smallest interval lengths.

Keywords:

• stratified sampling
• two-phase sampling
• quantile
• variance estimation

2000 AMS Subject Classification :

• 62D05

Acknowledgements

This work was partially supported by Ministerio de Educación y Ciencia (contract No. MTM2009-10055).