Cevapsızlık Durumunda Sıralı Küme Örneklemesi ve Medyan Sıralı Küme Örneklemesi Altında İki Yardımcı Değişkene Dayalı Regresyon Tahmincisi

Yıl 2025, Cilt: 21 Sayı: 2, 309 - 324, 01.11.2025

Ayşenur Akın Vargeloğlu , Yaprak Arzu Özdemir

https://doi.org/10.17134/khosbd.1758912

Öz

Cevapsızlık durumu, uygulamalı araştırmalarda sıkça karşılaşılan başlıca sorunlardan biridir ve yığın parametrelerinin güvenilir biçimde tahmin edilmesini önemli ölçüde olumsuz etkiler. Bu çalışmada, cevapsızlık durumunda, Sıralı Küme Örnekleme ve Medyan Sıralı Küme Örnekleme yöntemleri altında, iki yardımcı değişkenden yararlanan regresyon tahmin edicileri önerilmiştir. Önerilen tahmin edicilerin etkinliğini değerlendirmek amacıyla kapsamlı bir simülasyon çalışması gerçekleştirilmiştir. Ayrıca, bu tahmin edicilerin uygulanabilirliği gerçek bir veri seti üzerinde gösterilmiştir. Değerlendirme sonuçlarına göre, önerilen tahmin ediciler, klasik regresyon ve oran tahmin edicilerine kıyasla daha yüksek etkinlik göstermiştir.

Anahtar Kelimeler

Cevapsızlık , Sıralı Küme Örneklemesi , Regresyon tahmin Edicisi , Medyan Sıralı Küme Örneklemesi

Regression Estimator Based on Two Auxiliary Variables Under Ranked Set Sampling and Median Ranked Set Sampling in the Presence of Non-Response

Öz

Non-response is one of the major issues frequently encountered in applied research, and it significantly impairs the reliable estimation of population parameters. In this study, regression estimators utilizing information from two auxiliary variables are proposed under Ranked Set Sampling and Median Ranked Set Sampling methods in the presence of non-response. A comprehensive simulation study was conducted to evaluate the efficiency of the proposed estimators. In addition, the applicability of these estimators was demonstrated through a real data application. Based on the evaluation results, the proposed estimators demonstrated higher efficiency than the conventional regression and ratio estimators.

Anahtar Kelimeler

Non-response , Ranked Set Sampling , Regression Estimator , Median Ranked Set Sampling

Kaynakça

• [1] C. N. Bouza-Herrera, “Handling missing data in ranked set sampling,” Springer, 2013.
• [2] M. H. Hansen and W. N. Hurwitz, “The problem of non-response in sample surveys,” Journal of the American Statistical Association, vol. 41, no. 236, pp. 517–529, 1946. doi: 10.1080/01621459.1946.10501894
• [3] P. S. Levy and S. Lemeshow, “Sampling of populations: Methods and applications,” Wiley Series in Probability and Statistics, 1999.
• [4] C. B. Metin and Y. A. Özdemir, “Nonresponse error and examining the effects on the estimation of population mean: Two subpopulation study,” Süleyman Demirel University Journal of Natural and Applied Sciences, vol. 18, no. 2, pp. 54–63, 2014.
• [5] M. Yaqub and J. Shabbir, “Estimation of population distribution function in the presence of non-response,” Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 2, 2018. doi: 10.15672/HJMS.201613118919
• [6] S. Ahmad, S. Hussain, M. Aamir, F. Khan, M. N. Alshahrani, and M. Alqawba, “Estimation of finite population mean using dual auxiliary variable for non-response using simple random sampling,” AIMS Mathematics, vol. 7, no. 3, 2022. doi: 10.3934/math.2022256
• [7] U. Shahzad, M. Hanif, and N. Koyuncu, “Some new classes of estimators under linear systematic sampling in absence and presence of non-response,” Journal of Statistics and Management Systems, vol. 22, no. 6, pp. 1067–1091, 2019. doi: 10.1080/09720510.2018.1564582
• [8] N. Koyuncu, “Efficient estimators of population mean using auxiliary attributes,” Applied Mathematics and Computation, vol. 218, no. 22, pp. 10900–10905, 2012. doi: 10.1016/j.amc.2012.04.050
• [9] A. K. P. C. Swain, “On an improved ratio type estimator of finite population mean in sample surveys,” Revista Investigación Operacional, vol. 35, no. 1, pp. 49–57, 2014.
• [10] U. Shahzad, M. Hanif, N. Koyuncu, and A. V. Garcia Luengo, “A family of ratio estimators in stratified random sampling utilizing auxiliary attribute alongside the nonresponse issue,” Journal of Statistical Theory and Applications, vol. 18, no. 1, pp. 12–25, 2019. Doi: 10.2991/jsta.d.190306.002
• [11] G. A. McIntyre, “A method for unbiased selective sampling, using ranked sets,” The American Statistician, vol. 59, no. 3, pp. 230–232, 2005.
• [12] C. N. Bouza, “Ranked set sampling procedures for the estimation of the population mean under non-responses: A comparison,” vol. 31, 2010.
• [13] L. Khan and J. Shabbir, “Improved ratio-type estimators of population mean in ranked set sampling using two concomitant variables,” Pakistan Journal of Statistics and Operation Research, vol. 12, no. 3, 2016. doi: 10.18187/pjsor.v12i3.1271
• [14] S. Ahmed and J. Shabbir, “Ranked set sampling with scrambled response model to subsample non-respondents,” Brazilian Journal of Probability and Statistics, vol. 31, no. 1, pp. 179–193, 2017. doi: 10.1214/16-B
• [15] S. A. Rehman and J. Shabbir, “An efficient class of estimators for finite population mean in the presence of nonresponse under ranked set sampling (RSS),” PLOS ONE, vol. 17, no. 12, e0277232, 2022. doi: 10.1371/journal.pone.0277232
• [16] M. Fatima, S. H. Shahbaz, M. Hanif, and M. Q. Shahbaz, “A modified regression-cum-ratio estimator for finite population mean in presence of nonresponse using ranked set sampling,” AIMS Mathematics, vol. 7, no. 4, 2022. doi: 10.3934/math.2022361
• [17] S. Mohanty, “Combination of regression and ratio estimate,” Journal of Indian Statistical Association, vol. 5, pp. 16–19, 1967.
• [18] S. A. Rehman, L. A. Al-Essa, J. Shabbir, and Z. Khan, “On the efficiency of paired ranked set sampling for estimating the population mean in the presence of non-response,” Scientific Reports, vol. 14, no. 1, 2024.
• [19] S. Malik, Kanika, and Atul, “An improvement in regression estimator through exponential estimator using two auxiliary variables,” Journal of Reliability and Statistical Studies, vol. 16, no. 2, pp. 329–335, 2023.
• [20] H. A. Muttlak, “Median ranked set sampling,” Journal of Applied Statistical Sciences, vol. 6, no. 4, pp. 245–255, 1997.
• [21] W. G. Cochran, “Sampling techniques, 3rd ed.,” New York: John Wiley and Sons, 1977.
• [22] S. Singh, “Advanced sampling theory with applications: How Michael “selected” Amy” Springer Science & Business Media, 2003.
• [23] R. Alharbi, M. S. Mustafa, A. Al Mutairi, M. Hussein, M. Yusuf, A. Elshenawy, and S. G. Nassr, “Enhancing mean estimators in median ranked set sampling with dual auxiliary information,” Heliyon, vol. 9, no. 11, e21427, 2023. doi: 10.1016/j.heliyon.2023.e21427
• [24] N. Koyuncu, “Regression estimators in ranked set, median ranked set and neoteric ranked set sampling,” Pakistan Journal of Statistics and Operation Research, vol. 14, no. 1, pp. 89–94, 2018.
• [25] W. J. Nash, “The population biology of abalone (Haliotis species) in Tasmania. I. Blacklip abalone from the north coast and islands of Bass Strait,” 1994.