Two-layer median ranked set sampling
Yıl 2019,
Cilt: 48 Sayı: 5, 1560 - 1569, 08.10.2019
Begum Kara Gulay
,
Neslihan Demirel
Öz
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.
Kaynakça
- [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.
Yıl 2019,
Cilt: 48 Sayı: 5, 1560 - 1569, 08.10.2019
Begum Kara Gulay
,
Neslihan Demirel
Kaynakça
- [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.