Sankhya A

, Volume 77, Issue 2, pp 408–432 | Cite as

Nonparametric Confidence Intervals for Quantiles with Randomized Nomination Sampling

  • Mohammad Nourmohammadi
  • Mohammad Jafari Jozani
  • Brad C. Johnson


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.

Keywords and phrases.

Confidence interval infinite population order statistics nomination sampling imperfect ranking. 

AMS (2000) subject classification.

Primary 62G15 Secondary 62D05 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Boyles R.A. and Samaniego F.J. (1986). Estimating a distribution function based on nomination sampling. J. Am. Stat. Assoc. 81, 101–133.MathSciNetCrossRefGoogle Scholar
  2. Burgette L.F. and Reinter J.P. (2012). Modeling adverse birth outcomes via confirmatory factor quantile regression. Biometrics 68, 92–100.MathSciNetCrossRefzbMATHGoogle Scholar
  3. David H.A. and Nagaraja H.N. (2003) Order statistics, 3rd edn. Wiley.Google Scholar
  4. Jafari Jozani M. and Johnson B.C. (2012). Randomized nomination sampling for finite populations. J. Stat. Plann. Infer. 142, 2103–2115.MathSciNetCrossRefzbMATHGoogle Scholar
  5. Jafari Jozani M. and Mirkamali S.J. (2011). Control charts for attributes with maxima nominated samples. J. Stat. Plann. Infer. 141, 2386–2398.MathSciNetCrossRefzbMATHGoogle Scholar
  6. Jafari Jozani M. and Mirkamali S.J. (2010). Improved attribute acceptance sampling plans based on maxima nomination sampling. J. Stat. Plann. Infer. 140, 2448–2460.MathSciNetCrossRefzbMATHGoogle Scholar
  7. Kvam P.H. (2003). Ranked set sampling based on binary water quality data with covariates. J. Agric. Biol. Environ. Stat. 8, 271–279.CrossRefGoogle Scholar
  8. Kvam P.H. and Samaniego F.J. (1993). On estimating distribution functions using nomination samples. J. Am. Stat. Assoc. 88, 1317–1322.MathSciNetCrossRefzbMATHGoogle Scholar
  9. Murff E.J.T. and Sager T.W. (2006). The relative efficiency of ranked set sampling in ordinary least squares regression. Environ. Ecol. Stat. 13, 41–51.MathSciNetCrossRefGoogle Scholar
  10. Ozturk O., Bilgin O., and Wolfe D.A. (2005). Estimation of population mean and variance in flock management: a ranked set sampling approach in a finite population setting. J. Stat. Comput. Simul. 11, 905–919.MathSciNetCrossRefGoogle Scholar
  11. Nourmohammadi M., Jafari Jozani M., and Johnson B. (2014). Confidence interval for quantiles in finite populations with randomized nomination sampling. Comput. Stat. Data Anal. 73, 112–128.MathSciNetCrossRefGoogle Scholar
  12. Tiwari R.C. (1988). Bayes estimation of a distribution under a nomination sampling. IEEE Trans. Reliab. 37, 558–561.CrossRefzbMATHGoogle Scholar
  13. Tiwari R.C. and Wells M.T. (1989). Quantile estimation based on nomination sampling. IEEE Trans. Reliab. 38, 612–614.CrossRefzbMATHGoogle Scholar
  14. Yu P.L. and Lam K. (1997). Regression estimator in ranked set sampling. Biometrics 53, 1070–1080.CrossRefzbMATHGoogle Scholar
  15. Wells M.T. and Tiwari R.C. (1990) Estimating a distribution function based on minima-nomination sampling. In Topics in statistical dependence, volume 16 of IMS Lecture Notes Monogr. Ser. Inst. Math. Statist., Hayward, pp. 471–479.Google Scholar
  16. Willemain T.R. (1980). Estimating the population median by nomination sampling. J. Am. Stat. Assoc. 75, 908–911.CrossRefGoogle Scholar

Copyright information

© Indian Statistical Institute 2014

Authors and Affiliations

  • Mohammad Nourmohammadi
    • 1
  • Mohammad Jafari Jozani
    • 1
  • Brad C. Johnson
    • 1
  1. 1.Department of StatisticsUniversity of ManitobaWinnipegCanada

Personalised recommendations