On kernel-based estimation of distribution function and its quantiles based on ranked set sampling

Abstract

This paper proposes to use the convex combination of several kernel estimators based on the ranked set sampling (RSS) scheme for estimating the underlying distribution function to construct more efficient quantiles estimation. Several different estimators of quantile function based on the simple random sampling and ranked set sampling are provided. The variance and mean-squared error of the proposed estimators are derived as explicit forms. Theoretical derivation and an intensive simulation study are used to compare the performance of the proposed method with other methods in the literature. The effect of imperfect rankings on the performance of the proposed estimators is investigated. Real data example from the China Health and Nutrition Survey is used to illustrate our proposed approach. Some discussions using another two real data are presented. It observes that the proposed estimators have different behaviours with respect to symmetric and asymmetric distributions.

Keywords:

• Convex combination
• kernel-based estimation
• quantile function
• ranked set sampling

Acknowledgments

The authors express their sincere thanks to the anonymous referees and the associate editor for their useful comments and constructive criticisms on the original version of this manuscript, which led to this considerably improved version.

Disclosure statement

No potential conflict of interest was reported by the author(s).