Distribution function estimation using concomitant-based ranked set sampling

Year 2018, Volume: 47 Issue: 3, 755 - 761, 01.06.2018

Ehsan Zamanzade M. Mahdizadeh

Abstract

Ranked set sampling (RSS) is a data collection method designed to exploit auxiliary ranking information. In this paper, a new estimator of distribution function is proposed when RSS is done by using a concomitant variable. It is shown by simulation study that the alternative estimator can be considerably more efficient than the standard one, especially when the rankings are perfect.

Keywords

Relative efficiency, Concomitant variable, Judgment ranking

References

• Chen, Z., Bai, Z., and Sinha, B.K. Ranked set sampling: Theory and Applications, Springer, New York, 2004.
• Dell, T.R., and Clutter, J.L. Ranked set sampling theory with order statistics background, Biometrics 28(2), 545-555, 1972.
• Frey, J., Ozturk, O., and Deshpande, J.V., Nonparametric tests for perfect judgment rank- ings, Journal of the American Statistical Association 102(478), 708-717, 2007.
• Frey, J. A note on ranked-set sampling using a covariate, Journal of Statistical Planning and Inference 141(2), 809-816, 2011.
• Li,T., and Balakrishnan, N. Some simple nonparametric methods to test for perfect ranking in ranked set sampling. Journal of Statistical Planning and Inference 138(5), 1325-1338, 2008.
• McIntyre, G.A. A method for unbiased selective sampling using ranked set sampling, Aus- tralian Journal of Agricultural Research, 3, 385-390, 1952.
• MacEachern, S.N., Ozturk, O., Wolfe, D.A. and Stark, G.V. A new ranked set sample estimator of variance, Journal of the Royal Statistical Society: Series B. 64(2), 177-188, 2002.
• Platt, W.J., Evans, G.M., and Rathbun, S.L. The population dynamics of a long-lived conifer (Pinus palustris), American Naturalist 131, 491525, 1988.
• Robertson, T., Wright, F.T., and Dykstra, R.L. Order Restricted Statistical Inference, Wi- ley, New York, 1988.
• Stokes, S.L. Estimation of variance using judgment ordered ranked set samples, Biometrics 36(1), 35-42, 1980.
• Stokes, S.L., and Sager, T.W. Characterization of a Ranked-Set Sample with Application to Estimating Distribution Functions, Journal of the American Statistical Association 83(402), 374-381, 1988.
• Takahasi, K. and Wakimoto, K. On unbiased estimates of the population mean based on the sample stratied by means of ordering, Annals of the Institute of Statistical Mathematics 20, 1-31, 1968.
• Vock, M., and Balakrishnan, N. A. Jonckheere-Terpstra-type test for perfect ranking in balanced ranked set sampling, Journal of Statistical Planning and Inference 141(2), 624- 630, 2011.
• Zamanzade, E. , Arghami, N.R., Vock, M. Permutation-based tests of perfect ranking, Sta- tistics & Probability Letters 82(12), 2213-2220, 2012.
• Zamanzade, E., Arghami, N.R., and Vock, M. A parametric test of perfect ranking in bal- anced ranked set sampling, Communications in Statistics: Theory and Methods 43(21), 4589-4611, 2014.
• Zamanzade, E,. and Vock, M. Variance estimation in ranked set sampling using a concomi- tant variable, Statistics & Probability Letters 105, 1-5, 2015.
• Zamanzade, E,. and Mohammadi, M. Some modied mean estimators in ranked set sampling using a covariate, Journal of Statistical Theory and Applications 15(2), 142-152, 2016.