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.
Similar content being viewed by others
References
Boyles R.A. and Samaniego F.J. (1986). Estimating a distribution function based on nomination sampling. J. Am. Stat. Assoc. 81, 101–133.
Burgette L.F. and Reinter J.P. (2012). Modeling adverse birth outcomes via confirmatory factor quantile regression. Biometrics 68, 92–100.
David H.A. and Nagaraja H.N. (2003) Order statistics, 3rd edn. Wiley.
Jafari Jozani M. and Johnson B.C. (2012). Randomized nomination sampling for finite populations. J. Stat. Plann. Infer. 142, 2103–2115.
Jafari Jozani M. and Mirkamali S.J. (2011). Control charts for attributes with maxima nominated samples. J. Stat. Plann. Infer. 141, 2386–2398.
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.
Kvam P.H. (2003). Ranked set sampling based on binary water quality data with covariates. J. Agric. Biol. Environ. Stat. 8, 271–279.
Kvam P.H. and Samaniego F.J. (1993). On estimating distribution functions using nomination samples. J. Am. Stat. Assoc. 88, 1317–1322.
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.
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.
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.
Tiwari R.C. (1988). Bayes estimation of a distribution under a nomination sampling. IEEE Trans. Reliab. 37, 558–561.
Tiwari R.C. and Wells M.T. (1989). Quantile estimation based on nomination sampling. IEEE Trans. Reliab. 38, 612–614.
Yu P.L. and Lam K. (1997). Regression estimator in ranked set sampling. Biometrics 53, 1070–1080.
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.
Willemain T.R. (1980). Estimating the population median by nomination sampling. J. Am. Stat. Assoc. 75, 908–911.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13171-014-0062-3