Ratio Type Estimators of the Population Mean Based on Ranked Set Sampling

Authors: Said Ali Al-Hadhrami

Abstract:

Ranked set sampling (RSS) was first suggested to increase the efficiency of the population mean. It has been shown that this method is highly beneficial to the estimation based on simple random sampling (SRS). There has been considerable development and many modifications were done on this method. When a concomitant variable is available, ratio estimation based on ranked set sampling was proposed. This ratio estimator is more efficient than that based on SRS. In this paper some ratio type estimators of the population mean based on RSS are suggested. These estimators are found to be more efficient than the estimators of similar form using simple random sample.

Keywords: Bias, Efficiency, Ranked Set Sampling, Ratio Type Estimator

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1071402

References:

[1] McIntyre, G. A., (1952). A method of unbiased selective sampling, using ranked sets, Australian J. Agricultural Research, 3, 385-390.
[2] Takahasi, K. and Wakimoto, K. (1968). On unbiased estimates of the population mean based on the sample stratified by means of ordering. Annals of the Institute of Statistical Mathematics 20, 1-31.
[3] Dell, T.R. and Clutter, J.L. (1972). Ranked Set Sampling Theory with Order Statistics Background. Biometrics 28, 545-555.
[4] David, H.A. and Lavine, D.N. (1972). Ranked set sampling in the presence of judgment error. Biometrics 28, 553-555.
[5] Dell, T.R., and Halls, L.K. (1966). Trial of ranked set sampling for forage yields. Forest Science 12, 22-32.
[6] Evans, M.J. (1967). Application of ranked set sampling to regeneration survey in areas direct- seeded to longleaf pine. Master thesis, School of Forestry and Wildlife Management, Louisiana State University, Baton Rouge, Louisiana.
[7] Martin,W.L., Sarik,T.L., Oderwald, R.G., and Smith, D.W.(1980). Evaluation of ranked set sampling for estimating shrub phytomass in Appalachian oak forests. Publication Number FWS-4-80, School of Forestry and Wildlife Resources, Virginia Polytechnic Institute and State University, Blacksburg, Verginia.
[8] Cobby, J.M., Ridout, M.S., Bassett, P.J. and Large, R.V. (1985). An investigation into the use of ranked set sampling on grass and grasscocer swards, Grass and Forage Science,Vol.40, 257-263.
[9] Johnson, G.D., Patil, G.P. and A.K.Sinha (1993), Ranked set sampling for vegetation research, Abstracta Botanica,Vol.17, 87-102.
[10] Yu, p.L.H. and Lam, K. (1997) Regression estimator in ranked set sampling, Biometrics, 53, 1070-1080.
[11] Al-Saleh, M.F and Al-Shrafat, K.(2001). Estimation of average milk yield using ranked set sampling, Environmetrics, 12, 395-399
[12] Chen, Z., Bai, Z.D. and Sinha, B.K., (2004). Ranked Set Sampling: Theory and Application.New York: Springer-verlag.
[13] Stokes, S.L. (1977). Ranked set sampling with concomitant variables. Communications in Statistics- Theory and Methods 6, 1207-1211.
[14] Samawi, H.M. and Muttlak, H.A. (1996). Estimation of ratio Using Ranked Set Sampling. The Biometrical Journal. Vol.36, 753-764.
[15] Kadilar, C., H.Cingi,(2004). Ratio estimators in simple random sampling, Applied Mathematics and computation 151, 893-902.