Abstract
We consider nonparametric interval estimation for the population mean and quantiles based on a ranked set sample. The asymptotic distributions of the empirical log likelihood ratio statistic for the mean and quantiles are derived. Interval estimates of the population mean and quantiles are obtained by inverting the likelihood ratio statistic. Simulations are carried out to investigate and compare the performance of the empirical likelihood intervals with other known intervals.
Similar content being viewed by others
References
Adimari G (1998) An empirical likelihood statistic for quantiles. J Stat Comput Simul 60: 85–95
Chen Z (2000) On ranked-set sample quantiles and their applications. J Stat Plan Inference 83: 125–135
Chen Z, Bai Z, Sinha B (2004) Ranked set sampling: theory and applications. Springer, Heidelberg
McIntyre GA (1952) A method of unbiased selective sampling, using ranked sets. Aust J Agric Res 3: 385–390
Owen AB (1990) Empirical likelihood ratio confidence regions. Ann Stat 18: 90–12
Owen AB (2001) Empirical likelihood. Chapman & Hall
Qin G, Tsao M (2002) Empirical likelihood ratio confidence interval for the trimmed mean. Commun Stat Theory Methods 31(12): 2197–2208
Takahasi K, Wakimoto K (1968) On unbiased estimates of the population mean based on the sample stratified by means of ordering. Ann Inst Stat Math 20: 1–31
Tsao M (2004) A new method of calibration for the empirical loglikelihood ratio. Stat Probab Lett 68: 305–314
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Baklizi, A. Empirical likelihood intervals for the population mean and quantiles based on balanced ranked set samples. Stat Methods Appl 18, 483–505 (2009). https://doi.org/10.1007/s10260-008-0105-9
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10260-008-0105-9