Distribution function estimation using concomitant-based ranked set sampling

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

1. Chen, Z., Bai, Z., and Sinha, B.K. Ranked set sampling: Theory and Applications, Springer, New York, 2004.
2. Dell, T.R., and Clutter, J.L. Ranked set sampling theory with order statistics background, Biometrics 28(2), 545-555, 1972.
3. 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.
4. Frey, J. A note on ranked-set sampling using a covariate, Journal of Statistical Planning and Inference 141(2), 809-816, 2011.
5. 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.
6. McIntyre, G.A. A method for unbiased selective sampling using ranked set sampling, Aus- tralian Journal of Agricultural Research, 3, 385-390, 1952.
7. 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.
8. 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.

9. Robertson, T., Wright, F.T., and Dykstra, R.L. Order Restricted Statistical Inference, Wi- ley, New York, 1988.
10. Stokes, S.L. Estimation of variance using judgment ordered ranked set samples, Biometrics 36(1), 35-42, 1980.
11. 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.
12. 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.
13. 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.
14. Zamanzade, E. , Arghami, N.R., Vock, M. Permutation-based tests of perfect ranking, Sta- tistics & Probability Letters 82(12), 2213-2220, 2012.
15. 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.
16. Zamanzade, E,. and Vock, M. Variance estimation in ranked set sampling using a concomi- tant variable, Statistics & Probability Letters 105, 1-5, 2015.
17. 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.