Quantile Estimation in the Presence of Auxiliary Information under Negatively Associated Samples

Abstract

In this article, we apply the empirical likelihood technique to propose a new class of quantile estimators in the presence of some auxiliary information under negatively associated samples. It is shown that the proposed quantile estimators are asymptotically normally distributed with smaller asymptotic variances than those of the usual quantile estimators. It is also shown that blocking technique is an useful tool in estimating asymptotic variance under negatively associated samples, which makes it possible to construct normal approximation based confidence intervals for quantiles.

Keywords:

• Empirical likelihood
• Negatively associated sample
• Quantile
• Relative efficiency

Mathematics Subject Classification:

• Primary 62G05
• Secondary 62E20

Acknowledgement

This work was partially supported by the National Natural Science Foundation of China (10971038), the Natural Science Foundation of Guangxi (2010 GXNSFA 013117), and the New Century Ten, Hundred and Thousand Talents Project of Guangxi. The authors are thankful to the referees for constructive suggestions.