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Nonparametric Confidence Intervals for Quantiles with Randomized Nomination Sampling

Abstract

Rank-based sampling methods have a wide range of applications in environmental and ecological studies as well as medical research and they have been shown to perform better than simple random sampling (SRS) for estimating several parameters in finite populations. In this paper, we obtain nonparametric confidence intervals for quantiles based on randomized nomination sampling (RNS) from continuous distributions. The proposed RNS confidence intervals provide higher coverage probabilities and their expected length, especially for lower and upper quantiles, can be substantially shorter than their counterparts under SRS design. We observe that a design parameter associated with the RNS design allows one to construct confidence intervals with the exact desired coverage probabilities for a wide range of population quantiles without the use of randomized procedures. Theoretical results are augmented with numerical evaluations and a case study based on a livestock data set. Recommendations for choosing the RNS design parameters are made to achieve shorter RNS confidence intervals than SRS design and these perform well even when ranking is imperfect.

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Correspondence to Mohammad Jafari Jozani.

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Nourmohammadi, M., Jafari Jozani, M. & Johnson, B.C. Nonparametric Confidence Intervals for Quantiles with Randomized Nomination Sampling. Sankhya A 77, 408–432 (2015). https://doi.org/10.1007/s13171-014-0062-3

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  • DOI: https://doi.org/10.1007/s13171-014-0062-3

Keywords and phrases.

  • Confidence interval
  • infinite population
  • order statistics
  • nomination sampling
  • imperfect ranking.

AMS (2000) subject classification.

  • Primary 62G15
  • Secondary 62D05