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Sıralı küme örneklemesi altında farklı bootstrap yöntemleri ile yığın ortalaması için güven aralığı

Year 2017, , 1394 - 1407, 01.12.2017
https://doi.org/10.16984/saufenbilder.295879

Abstract

Sıralı Küme Örneklemesi, ilgili
değişken bakımından örnekleme birimlerini ölçmenin maliyet veya zaman
bakımından zor olduğu durumlarda Basit Tesadüfi Örnekleme’ye göre daha etkin
bir örnekleme yöntemidir. Güven aralığı ve hipotez testi gibi istatistiksel
çıkarımlar yapılırken dağılım varsayımına ihtiyaç duyulur. Dağılım bilgisinin
olmadığı veya istatistiksel çıkarımın mümkün olmadığı durumlarda ise yeniden
örnekleme teknikleri kullanılabilir. Bootstrap yöntemi de bunlardan biridir. Bu
çalışmada, Sıralı Küme Örneklemesinde yığın ortalamasına ilişkin güven aralığı
üç farklı bootstrap yöntemi kullanılarak ele alınmıştır. Bu yöntemler
kullanılarak güven aralığı kapsama olasılıkları ve güven aralığı genişlikleri
farklı dağılımlar kullanılarak simülasyon yoluyla elde edilmiştir. Simetrik
olmayan dağılımlara göre simetrik dağılımlar için elde edilen güven aralığı
kapsama olasılıklarının belirlenen güvenilirlik düzeyine daha yakın sonuçlar
verdiği görülmüştür.

References

  • [1] McIntyre, G.A.,“A method of unbiased selective sampling using ranked sets”. Australian Journal of Agricaltural Research, vol. 3, 385-390, 1952.
  • [2] Takahasi , K.;Wakimoto, K.,“On Unbiased estimates of the population mean based on the sample stratified by means of ordering”. Annals of The Institude of Statistical Mathematics, vol. 21, 249-255, 1968.
  • [3] Dell,D.R.; Clutter, J.L.,“Ranked set sampling theory with order statistics background”. Biometrics, vol. 28, 545-555, 1972
  • [4] Shen, W. H.,“On estimation of a log-normal mean using a ranked set sample”. Sankhya, vol. 54,B :323-333, 1994.
  • [5] Bhoj, D.S.; Ahsanullah, M.,“Estimation of parameters of the generalized geometric distribution using ranked set sampling”. Biometrics, 52: 685-694, 1996.
  • [6] Deshpande, JV; Frey, J.; Özturk, Ö.,“Nonparametric ranked-set sampling confidence intervals for quantiles of a finite population”. Environmental and Ecological Statistics, vol. 13, no. 1, pp. 25-40, 2006.
  • [7] Muttlak, H. A.; Abu-Dayyeh, W. A.; Al-Sawi, E.; Al-Momani. “Confidence interval estimation of the location and scale parameters of the logistic distribution using pivotal method”. Journal of Statistical Computaion and Simulation. vol. 81 Issue: 4 Pages: 391-409, 2011.
  • [8] Albatineh,A.N.; Golam Kibria, B.M.; Meredith L Wilcox; Bashar Zogheib, “Confidence interval estimation for the population coefficient of variation using ranked set sampling: a simulation study”. Journal of Applied Statistics, 41:4, 733-751, 2014.
  • [9] Aissa, A.O.; Ibrahim, K; Abu Dayyeh, W; Zin, W.Z.W. On the comparion of the interval estimation of the pareto parameter under simple random sampling and ranked set sampling, 2nd ISM Conference 2014, Malaysia.
  • [10] Özdemir, Y.A.; Ebegil, M; Gökpınar, F.,“A test statistic based on ranked set sampling for two normal means” Journal Communications in Statistics - Simulation and Computation (in press).2016.
  • [11] Efron, B. Bootstrap methods: Another look at Jackknife, Institute Of Mathematical Statistics, 7, 1-26, 1979.
  • [12] Hui, T.P.; Modarres, R; Zheng, G.,“Bootstrap confidence interval estimation of mean via ranked set sampling linear regression” Journal of the Statistical Computaion and Simulation. vol. 75 Issue:7 Pages:543-553,2005.
  • [13] Modarres, R.; Hui, T.P.; Zheng, G.,“Resampling methods for ranked set samples”, Computational Statistics and Data Analysis, 51, 1039-1050,2006.

Confidence interval for the population mean using different bootstrap methods under ranked set sampling

Year 2017, , 1394 - 1407, 01.12.2017
https://doi.org/10.16984/saufenbilder.295879

Abstract

Ranked Set Sampling is a more effective
sampling method than Simple Random Sampling when it is difficult to measure
sampling units in terms of cost or time. When statistical inferences such as
confidence interval and hypothesis testing are performed, distributional
assumption is required. Resampling techniques can be used when there is no
distributional information or it is imposible to make statistical inference.
The bootstrap method is one of these techniques. In this study, the confidence
interval for the population mean in Ranked Set Sampling are considered by using
three different bootstrap techniques. By using these methods, confidence interval
coverage probabilities and confidence interval widths are obtained by
simulation using different distributions. It is observed that confidence
interval coverage probabilities under symmetrical distributions are closer to
the nominal level than confidence interval coverage probabilities under
nonsymmetrical distributions..

References

  • [1] McIntyre, G.A.,“A method of unbiased selective sampling using ranked sets”. Australian Journal of Agricaltural Research, vol. 3, 385-390, 1952.
  • [2] Takahasi , K.;Wakimoto, K.,“On Unbiased estimates of the population mean based on the sample stratified by means of ordering”. Annals of The Institude of Statistical Mathematics, vol. 21, 249-255, 1968.
  • [3] Dell,D.R.; Clutter, J.L.,“Ranked set sampling theory with order statistics background”. Biometrics, vol. 28, 545-555, 1972
  • [4] Shen, W. H.,“On estimation of a log-normal mean using a ranked set sample”. Sankhya, vol. 54,B :323-333, 1994.
  • [5] Bhoj, D.S.; Ahsanullah, M.,“Estimation of parameters of the generalized geometric distribution using ranked set sampling”. Biometrics, 52: 685-694, 1996.
  • [6] Deshpande, JV; Frey, J.; Özturk, Ö.,“Nonparametric ranked-set sampling confidence intervals for quantiles of a finite population”. Environmental and Ecological Statistics, vol. 13, no. 1, pp. 25-40, 2006.
  • [7] Muttlak, H. A.; Abu-Dayyeh, W. A.; Al-Sawi, E.; Al-Momani. “Confidence interval estimation of the location and scale parameters of the logistic distribution using pivotal method”. Journal of Statistical Computaion and Simulation. vol. 81 Issue: 4 Pages: 391-409, 2011.
  • [8] Albatineh,A.N.; Golam Kibria, B.M.; Meredith L Wilcox; Bashar Zogheib, “Confidence interval estimation for the population coefficient of variation using ranked set sampling: a simulation study”. Journal of Applied Statistics, 41:4, 733-751, 2014.
  • [9] Aissa, A.O.; Ibrahim, K; Abu Dayyeh, W; Zin, W.Z.W. On the comparion of the interval estimation of the pareto parameter under simple random sampling and ranked set sampling, 2nd ISM Conference 2014, Malaysia.
  • [10] Özdemir, Y.A.; Ebegil, M; Gökpınar, F.,“A test statistic based on ranked set sampling for two normal means” Journal Communications in Statistics - Simulation and Computation (in press).2016.
  • [11] Efron, B. Bootstrap methods: Another look at Jackknife, Institute Of Mathematical Statistics, 7, 1-26, 1979.
  • [12] Hui, T.P.; Modarres, R; Zheng, G.,“Bootstrap confidence interval estimation of mean via ranked set sampling linear regression” Journal of the Statistical Computaion and Simulation. vol. 75 Issue:7 Pages:543-553,2005.
  • [13] Modarres, R.; Hui, T.P.; Zheng, G.,“Resampling methods for ranked set samples”, Computational Statistics and Data Analysis, 51, 1039-1050,2006.
There are 13 citations in total.

Details

Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Nurdan Yeniay

Yaprak Arzu Özdemir

FİKRİ Gökpınar

Publication Date December 1, 2017
Submission Date March 2, 2017
Acceptance Date September 5, 2017
Published in Issue Year 2017

Cite

APA Yeniay, N., Özdemir, Y. A., & Gökpınar, F. (2017). Confidence interval for the population mean using different bootstrap methods under ranked set sampling. Sakarya University Journal of Science, 21(6), 1394-1407. https://doi.org/10.16984/saufenbilder.295879
AMA Yeniay N, Özdemir YA, Gökpınar F. Confidence interval for the population mean using different bootstrap methods under ranked set sampling. SAUJS. December 2017;21(6):1394-1407. doi:10.16984/saufenbilder.295879
Chicago Yeniay, Nurdan, Yaprak Arzu Özdemir, and FİKRİ Gökpınar. “Confidence Interval for the Population Mean Using Different Bootstrap Methods under Ranked Set Sampling”. Sakarya University Journal of Science 21, no. 6 (December 2017): 1394-1407. https://doi.org/10.16984/saufenbilder.295879.
EndNote Yeniay N, Özdemir YA, Gökpınar F (December 1, 2017) Confidence interval for the population mean using different bootstrap methods under ranked set sampling. Sakarya University Journal of Science 21 6 1394–1407.
IEEE N. Yeniay, Y. A. Özdemir, and F. Gökpınar, “Confidence interval for the population mean using different bootstrap methods under ranked set sampling”, SAUJS, vol. 21, no. 6, pp. 1394–1407, 2017, doi: 10.16984/saufenbilder.295879.
ISNAD Yeniay, Nurdan et al. “Confidence Interval for the Population Mean Using Different Bootstrap Methods under Ranked Set Sampling”. Sakarya University Journal of Science 21/6 (December 2017), 1394-1407. https://doi.org/10.16984/saufenbilder.295879.
JAMA Yeniay N, Özdemir YA, Gökpınar F. Confidence interval for the population mean using different bootstrap methods under ranked set sampling. SAUJS. 2017;21:1394–1407.
MLA Yeniay, Nurdan et al. “Confidence Interval for the Population Mean Using Different Bootstrap Methods under Ranked Set Sampling”. Sakarya University Journal of Science, vol. 21, no. 6, 2017, pp. 1394-07, doi:10.16984/saufenbilder.295879.
Vancouver Yeniay N, Özdemir YA, Gökpınar F. Confidence interval for the population mean using different bootstrap methods under ranked set sampling. SAUJS. 2017;21(6):1394-407.

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