Rank-based sampling designs are powerful alternatives to simple random sampling (SRS) and often provide large improvements in the precision of estimators. In many environmental, ecological, agricultural, industrial and/or medical applications the interest lies in sampling designs that are cheaper than SRS and provide comparable estimates. In this paper, we propose a new variation of ranked set sampling (RSS) for estimating the population mean based on the random selection technique to measure a smaller number of observations than RSS design. We study the properties of the population mean estimator using the proposed design and provide conditions under which the mean estimator performs better than SRS and some existing rank-based sampling designs. Theoretical results are augmented with some numerical studies and a real-life example, where we also study the performance of our proposed design under perfect and imperfect ranking situations.
Mean estimation Order statistics Random selection Ranked set sampling
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We would like to thank the constructive comments by two anonymous referees and an associate editor which improved the quality and the presentation of our results. Mohammad Jafari Jozani gratefully acknowledges the research support of NSERC (Natural Sciences and Engineering Research Council of Canada).
Arnold BC, Balakrishnan N, Nagaraja HN (2008) A first course in order statistics, Classic edn. SIAM, PhiladelphiaCrossRefGoogle Scholar
Chen SH (1983) Ranked set sampling theory with selective probability vector. J Stat Plan Inference 8:161–174CrossRefGoogle Scholar
Chen Z, Bai Z, Sinha BK (2004) Ranked set sampling: theory and applications. Springer, New YorkCrossRefGoogle Scholar
Hatefi A, Jafari Jozani M (2017) An improved procedure for estimation of malignant breast cancer prevalence using partially rank ordered set samples with multiple concomitants. Stat Methods Med Res 26(6):2552–2566CrossRefPubMedGoogle Scholar
Hatefi A, Jafari Jozani M, Ozturk O (2015) Mixture model analysis of partially rank ordered set samples: estimating the age groups of fish from length-frequency data. Scand J Stat 42(2):848–871CrossRefGoogle Scholar
Israel GD (1992) Sampling the evidence of extension program impact. University of Florida Cooperative Extension Service, Institute of Food and Agriculture Sciences, EDISGoogle Scholar
Kvam PH (2003) Ranked set sampling based on binary water quality data with covariates. J Agric Biol Environ Stat 8(3):271–279CrossRefGoogle Scholar
Li D, Ni Chuiv N (1997) On the efficiency of ranked set sampling strategies in parametric estimation. Bull Calcutta Stat Assoc 47(185):23–42CrossRefGoogle Scholar
Li D, Sinha BK, Perron F (1999) Random selection in ranked set sampling and its applications. J Stat Plan Inference 76:185–201CrossRefGoogle Scholar
McIntyre GA (1952) A method for unbiased selective sampling, using ranked sets. Aust J Agric Res 3(4):385–390CrossRefGoogle Scholar
Ozturk O, Bilgin O, Wolfe DA (2005) Estimation of population mean and variance in flock management: a ranked set sampling approach in a finite population setting. J Stat Comput Simul 11:905–919CrossRefGoogle Scholar
Rahimov I, Muttlak HA (2003) Estimation of the population mean using random selection in ranked set samples. Stat Probab Lett 62:203–209CrossRefGoogle Scholar
Samawi HM, AlSagheer OA (2001) On the estimation of the distribution function using extreme and median ranked set sampling. Biometrical J 43(3):357–373CrossRefGoogle Scholar
Yanagawa T, Shirahata S (1976) Ranked set sampling theory with selective probability matrix. Aust J Stat 18:45–52CrossRefGoogle Scholar