Computational Statistics

, Volume 32, Issue 4, pp 1689–1725

# Nonparametric confidence intervals for ranked set samples

Original Paper

## Abstract

In this work, we propose several different confidence interval methods based on ranked-set samples. First, we develop bootstrap bias-corrected and accelerated method for constructing confidence intervals based on ranked-set samples. Usually, for this method, the accelerated constant is computed by employing jackknife method. Here, we derive an analytical expression for the accelerated constant, which results in reducing the computational burden of this bias-corrected and accelerated bootstrap method. The other proposed confidence interval approaches are based on a monotone transformation along with normal approximation. We also study the asymptotic properties of the proposed methods. The performances of these methods are then compared with those of the conventional methods. Through this empirical study, it is shown that the proposed confidence intervals can be successfully applied in practice. The usefulness of the proposed methods is further illustrated by analyzing a real-life data on shrubs.

## Keywords

Bootstrap Edgeworth expansion Bias corrected and accelerated Monotone transformations

## Notes

### Acknowledgements

We express our sincere thanks to the Associate Editor and the anonymous reviewers for their useful comments and suggestions on an earlier versions of this manuscript which led to this improved one.

## Supplementary material

180_2017_744_MOESM1_ESM.pdf (28 kb)
Supplementary material 1 (pdf 27 KB)
180_2017_744_MOESM2_ESM.txt (0 kb)
Supplementary material 2 (txt 0 KB)

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© Springer-Verlag GmbH Germany 2017

## Authors and Affiliations

• Santu Ghosh
• 1
• Arpita Chatterjee
• 2
• N. Balakrishnan
• 3
1. 1.Department of Biostatistics and EpidemiologyAugusta UniversityAugustaUSA
2. 2.Department of Mathematical SciencesGeorgia Southern UniversityStatesboroUSA
3. 3.Department of Mathematics and StatisticsMcMaster UniversityHamiltonCanada