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Two-layer median ranked set sampling

Year 2019, Volume: 48 Issue: 5, 1560 - 1569, 08.10.2019
https://doi.org/10.15672/hujms.466178

Abstract

In this article, we propose two-layer median ranked set sampling (TMRSS) design that combines median ranked set sampling (MRSS) and two-layer ranked set sampling (TRSS). Ranked set sampling (RSS) is an alternative sampling method that can improve the efficiency of estimators when exact measurement of response variable is either difficult, time consuming or expensive. Evaluation of the TMRSS performance for different distributions, set, and cycle sizes regarding mean and regression coefficients estimators and mean square of the regression model are carried out using Monte Carlo simulation study and real data application. The results indicate that estimators of TMRSS yields are either equivalent to or better than MRSS.

References

  • [1] A. I. Al-Omari and C. N. Bouza, Review of ranked set sampling: modifications and applications, Investigación Oper. 35 (3), 215-235, 2014.
  • [2] M. F. Al-Saleh and A. I. Al-Omari, Multistage ranked set sampling, J. Statist. Plann. Inference 102 (2), 273-286, 2002.
  • [3] B. Cetintav, G. Ulutagay, S. Gurler and N.Demirel, Mean estimation based on fwa using ranked set sampling with single and multiple rankers, in: International Confer- ence on Information Processing and Management of Uncertainty in Knowledge-Based Systems, 790-797, Springer, Cham, 2016.
  • [4] Z. Chen, Z. Bai and B. Sinha, Ranked set sampling: theory and applications, Springer Science & Business Media, 2003.
  • [5] Z. Chen and L. Shen, Two-layer ranked set sampling with concomitant variables, J. Statist. Plann. Inference 115 (1), 45-57, 2003.
  • [6] H. A. David and D. N. Levine, Ranked set sampling in the presence of judgment error, Biometrics 28, 553-555, 1972.
  • [7] T. R. Dell and J. L. Clutter, Ranked set sampling theory with order statistics back- ground, Biometrics, 545-555, 1972.
  • [8] J. Frey, Constrained nonparametric estimation of the mean and the CDF using ranked- set sampling with a covariate, Ann. Inst. Statist. Math. 64 (2), 439-456, 2012.
  • [9] S. Hajighorbani and R. A. Saba, Stratified median ranked set sampling: Optimum and proportional allocations, Journal of Statistical Research of Iran 9, 87–102, 2012.
  • [10] B. Kara, Comparison of Efficiency of Two-Layer Median Ranked Set Sampling Using Concomitant Variables. Master’s thesis, Dokuz Eylul University, Turkey, 2015.
  • [11] L. Khan, J. Shabbir and S. Gupta, Unbiased ratio estimators of the mean in stratified ranked set sampling. Hacet. J. Math. Stat. 46 (6), 1151–1158, 2016.
  • [12] G. McIntyre, A method for unbiased selective sampling, using ranked sets, Australian Journal of Agricultural Research 3 (4), 385–390, 1952.
  • [13] H. A. Muttlak, Median ranked set sampling, J. Appl. Statist. Sci. 6, 245–255, 1997.
  • [14] H. A. Muttlak, Median ranked set sampling with concomitant variables and a compar- ison with ranked set sampling and regression estimators, Environmetrics: The official journal of the International Environmetrics Society 9 (3), 255–267, 1998.
  • [15] W. J. Nash, T. L. Sellers, S. R. Talbot, A. J. Cawthorn and W. B.Ford, The population biology of abalone (haliotis species) in tasmania. i. blacklip abalone (h. rubra) from the north coast and islands of bass strait, Sea Fisheries Division, Technical Report (48), 1994.
  • [16] B. Sevinc, S. Gurler and B. Cetintav, Partial groups ranked set sampling and mean estimation, J. Stat. Comput. Simul. 88 (14), 2799-2810, 2018.
  • [17] K. Takahasi and K. Wakimoto, On unbiased estimates of the population mean based on the sample stratified by means of ordering, Ann. Inst. Statist. Math. 20 (1), 1–31, 1968.
  • [18] X. Wang, S. Ahn and J. Lim, Unbalanced ranked set sampling in cluster randomized studies, J. Statist. Plann. Inference 187, 1–16, 2017.
  • [19] E. Zamanzade and A. I. Al-Omari, New ranked set sampling for estimating the pop- ulation mean and variance, Hacet. J. Math. Stat. 45 (6), 1891-1905, 2016.
  • [20] E. Zamanzade and M. Mahdizadeh, A more efficient proportion estimator in ranked set sampling, Statist. Probab. Lett. 129, 28–33, 2017.
  • [21] E. Zamanzade and M. Mahdizadeh, Using ranked set sampling with extreme ranks in estimating the population proportion, Stat. Methods Med. Res., 13 pages, 2019, https://doi.org/10.1177/0962280218823793.
Year 2019, Volume: 48 Issue: 5, 1560 - 1569, 08.10.2019
https://doi.org/10.15672/hujms.466178

Abstract

References

  • [1] A. I. Al-Omari and C. N. Bouza, Review of ranked set sampling: modifications and applications, Investigación Oper. 35 (3), 215-235, 2014.
  • [2] M. F. Al-Saleh and A. I. Al-Omari, Multistage ranked set sampling, J. Statist. Plann. Inference 102 (2), 273-286, 2002.
  • [3] B. Cetintav, G. Ulutagay, S. Gurler and N.Demirel, Mean estimation based on fwa using ranked set sampling with single and multiple rankers, in: International Confer- ence on Information Processing and Management of Uncertainty in Knowledge-Based Systems, 790-797, Springer, Cham, 2016.
  • [4] Z. Chen, Z. Bai and B. Sinha, Ranked set sampling: theory and applications, Springer Science & Business Media, 2003.
  • [5] Z. Chen and L. Shen, Two-layer ranked set sampling with concomitant variables, J. Statist. Plann. Inference 115 (1), 45-57, 2003.
  • [6] H. A. David and D. N. Levine, Ranked set sampling in the presence of judgment error, Biometrics 28, 553-555, 1972.
  • [7] T. R. Dell and J. L. Clutter, Ranked set sampling theory with order statistics back- ground, Biometrics, 545-555, 1972.
  • [8] J. Frey, Constrained nonparametric estimation of the mean and the CDF using ranked- set sampling with a covariate, Ann. Inst. Statist. Math. 64 (2), 439-456, 2012.
  • [9] S. Hajighorbani and R. A. Saba, Stratified median ranked set sampling: Optimum and proportional allocations, Journal of Statistical Research of Iran 9, 87–102, 2012.
  • [10] B. Kara, Comparison of Efficiency of Two-Layer Median Ranked Set Sampling Using Concomitant Variables. Master’s thesis, Dokuz Eylul University, Turkey, 2015.
  • [11] L. Khan, J. Shabbir and S. Gupta, Unbiased ratio estimators of the mean in stratified ranked set sampling. Hacet. J. Math. Stat. 46 (6), 1151–1158, 2016.
  • [12] G. McIntyre, A method for unbiased selective sampling, using ranked sets, Australian Journal of Agricultural Research 3 (4), 385–390, 1952.
  • [13] H. A. Muttlak, Median ranked set sampling, J. Appl. Statist. Sci. 6, 245–255, 1997.
  • [14] H. A. Muttlak, Median ranked set sampling with concomitant variables and a compar- ison with ranked set sampling and regression estimators, Environmetrics: The official journal of the International Environmetrics Society 9 (3), 255–267, 1998.
  • [15] W. J. Nash, T. L. Sellers, S. R. Talbot, A. J. Cawthorn and W. B.Ford, The population biology of abalone (haliotis species) in tasmania. i. blacklip abalone (h. rubra) from the north coast and islands of bass strait, Sea Fisheries Division, Technical Report (48), 1994.
  • [16] B. Sevinc, S. Gurler and B. Cetintav, Partial groups ranked set sampling and mean estimation, J. Stat. Comput. Simul. 88 (14), 2799-2810, 2018.
  • [17] K. Takahasi and K. Wakimoto, On unbiased estimates of the population mean based on the sample stratified by means of ordering, Ann. Inst. Statist. Math. 20 (1), 1–31, 1968.
  • [18] X. Wang, S. Ahn and J. Lim, Unbalanced ranked set sampling in cluster randomized studies, J. Statist. Plann. Inference 187, 1–16, 2017.
  • [19] E. Zamanzade and A. I. Al-Omari, New ranked set sampling for estimating the pop- ulation mean and variance, Hacet. J. Math. Stat. 45 (6), 1891-1905, 2016.
  • [20] E. Zamanzade and M. Mahdizadeh, A more efficient proportion estimator in ranked set sampling, Statist. Probab. Lett. 129, 28–33, 2017.
  • [21] E. Zamanzade and M. Mahdizadeh, Using ranked set sampling with extreme ranks in estimating the population proportion, Stat. Methods Med. Res., 13 pages, 2019, https://doi.org/10.1177/0962280218823793.
There are 21 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Statistics
Authors

Begum Kara Gulay 0000-0003-2926-2699

Neslihan Demirel 0000-0002-5394-4721

Publication Date October 8, 2019
Published in Issue Year 2019 Volume: 48 Issue: 5

Cite

APA Kara Gulay, B., & Demirel, N. (2019). Two-layer median ranked set sampling. Hacettepe Journal of Mathematics and Statistics, 48(5), 1560-1569. https://doi.org/10.15672/hujms.466178
AMA Kara Gulay B, Demirel N. Two-layer median ranked set sampling. Hacettepe Journal of Mathematics and Statistics. October 2019;48(5):1560-1569. doi:10.15672/hujms.466178
Chicago Kara Gulay, Begum, and Neslihan Demirel. “Two-Layer Median Ranked Set Sampling”. Hacettepe Journal of Mathematics and Statistics 48, no. 5 (October 2019): 1560-69. https://doi.org/10.15672/hujms.466178.
EndNote Kara Gulay B, Demirel N (October 1, 2019) Two-layer median ranked set sampling. Hacettepe Journal of Mathematics and Statistics 48 5 1560–1569.
IEEE B. Kara Gulay and N. Demirel, “Two-layer median ranked set sampling”, Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 5, pp. 1560–1569, 2019, doi: 10.15672/hujms.466178.
ISNAD Kara Gulay, Begum - Demirel, Neslihan. “Two-Layer Median Ranked Set Sampling”. Hacettepe Journal of Mathematics and Statistics 48/5 (October 2019), 1560-1569. https://doi.org/10.15672/hujms.466178.
JAMA Kara Gulay B, Demirel N. Two-layer median ranked set sampling. Hacettepe Journal of Mathematics and Statistics. 2019;48:1560–1569.
MLA Kara Gulay, Begum and Neslihan Demirel. “Two-Layer Median Ranked Set Sampling”. Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 5, 2019, pp. 1560-9, doi:10.15672/hujms.466178.
Vancouver Kara Gulay B, Demirel N. Two-layer median ranked set sampling. Hacettepe Journal of Mathematics and Statistics. 2019;48(5):1560-9.