Two-Stage Cluster Sampling with Ranked Set Sampling in the Secondary Sampling Frame

• Published in: Communications in statistics. Theory and methods Vol. 37; no. 15; pp. 2404 - 2415
• Main Authors: Nematollahi, N., Salehi M., M., Saba, R. Aliakbari
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 11-06-2008; Taylor & Francis
• Subjects: Exact sciences and technology; General topics; Linear inference, regression; Mathematics; Primary 62D05; Probability and statistics; Ranked set sampling; Sampling theory, sample surveys; Sciences and techniques of general use; Secondary 62F10; Simple random sampling; Statistics; Two-stage sampling; Unbiased estimator; Variance estimation; Two stage sampling; Secondary 62F10; Random sampling; Covariance analysis; Variance estimation; Unbiased estimator; Sampling without replacement; Two-stage sampling; Sampling design; Statistical simulation; Variance analysis; Mean estimation; Variance; Statistical method; Statistical regression; Simple random sampling; Unbiased estimation; Sampling theory; Ranked set sampling; Sample survey; Cluster sampling; Primary 62D05
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610920801919684

Motivated by a real-life problem, we develop a Two-Stage Cluster Sampling with Ranked Set Sampling (
TSCRSS
) design in the second stage for which we derive an unbiased estimator of population mean and its variance. An unbiased estimator of the variance of mean estimator is also derived. It is proved that the
TSCRSS
is more efficient-in the sense of having smaller variance-than the conventional two-stage cluster simple random sampling in which the second-stage sampling is with replacement. Using a simulation study on a real-life population, we show that the
TSCRSS
is more efficient than the conventional two-stage cluster sampling when simple random sampling without replacement is used in both stages.