Research Article
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Robust regression type estimators for body mass index under extreme ranked set and quartile ranked set sampling

Year 2024, Volume: 73 Issue: 2, 336 - 348, 21.06.2024

Arzu Ece Çetin , Nursel Koyuncu

https://doi.org/10.31801/cfsuasmas.1373759

Abstract

Robust regression-type estimators of population mean that use auxiliary variable information are proposed by considering robust methods under extreme ranked set sampling (ERSS) and quartile ranked set sampling (QRSS). We have used the data concerning body mass index (BMI) for 800 people in Turkey in 2014. The real data example is applied to see efficiency of the estimators in ERSS and QRSS designs and it is found that the proposed estimators are better in these designs than the classical ranked set sampling (RSS) design. In addition, mean square error (MSE) and percent relative efficiency (PRE) are used to compare the performance of the adapted and proposed estimators.

Keywords

Robust regression estimators extreme ranked set sampling quartile ranked set sampling percentage relative efficiency (PRE)

References

  • Ali, N., Ahmad, I., Hanif, M., Shahzad, U., Robust-regression-type estimators for improving mean estimation of sensitive variables by using auxiliary information, Communications in Statistics-Theory and Methods, 3 (2019), 385–390. https://doi.org/10.1080/03610926.2019.1645857
  • Bouza, C. N., Ranked set sampling for the product estimator, Rev. Invest. Oper, 29(3) (2008), 201–206.
  • Koyuncu, N., Regression estimators in ranked set, median ranked set and neoteric ranked set sampling, Pakistan Journal of Statistics and Operation Research, 14(1) (2018), 89–94. https://doi.org/10.18187/pjsor.v14i1.1825
  • Koyuncu, N., Al-Omari, A. I., Generalized robust-regression-type estimators under different ranked set sampling, Mathematical Sciences, (2020). https://doi.org/10.1007/s40096-020-00360-7
  • Long, C., Chen, W., Yang, R., Yao D., Ratio estimation of the population mean using auxiliary under the optimal sampling design, Probability in the Engineering and Informational Sciences, 3 (2022), 449–460. https://doi.org/10.1017/s0269964820000625
  • Mclntyre, G. A., A method for unbiased selective sampling, using ranked sets, Australian Journal of Agricultural Research, 3 (1952), 385–390. https://doi.org/10.1071/ar9520385
  • Mehta, N., Mandowara, V. A., A modified ratio-cum-product estimator of finite population mean using ranked set sampling, Communication in Statistics- Theory and Methods, 45(2) (2016), 267–276. https://doi.org/10.1080/03610926.2013.830748
  • Muttlak, H. A., Investigating the use of quartile ranked set samples for estimating the population mean, Applied Mathematics and Computation, 146 (2003), 437–443. https://doi.org/10.1016/s0096-3003(02)00595-7
  • Samawi, H. M., Muttlak, H. A., Estimation of ratio using rank set sampling, Biometrical Journal, 38 (1996), 753-764. https://doi.org/10.1002/bimj.4710380616
  • Samawi, H. M., Ahmed, M. S.,Abu-Dayyeh, W., Estimating the population mean using extreme ranked set sampling, Biometrical Journal, 38(5) (1996), 577–586. https://doi.org/10.1002/bimj.4710380506
  • Shahzad, U., Hanif, M., Koyuncu, N., Luengo, A. V. G., A regression type estimator for mean estimation under ranked set sampling alongside the sensitivity issue, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2) (2019), 2037–2049. https://doi.org/10.31801/cfsuasmas.586057
  • Shahzad, U., Al-Noor, N., H., Hanif, M., Sajjad, I., Muhammad, A. M., Imputation based mean estimators in case of missing data utilizing robust regression and variance–covariance matrices, Communications in Statistics-Simulation and Computation, (2020), 1–20. https://doi.org/10.1080/03610918.2020.1740266
  • Subzar, M., Bouza, C. N., Al-Omari, A. I., Utilization of different robust regression techniques for estimation of finite population mean in srswor in case of presence of outliers through ratio method of estimation, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 40(5) (2019), 600–609. https://doi.org/10.32604/cmc.2020.010230
  • Zaman, T., Bulut, H., Modified ratio estimators using robust regression methods, Communications in Statistics-Theory and Methods, 48(8) (2019), 2019–2048. https://doi.org/10.1080/03610926.2018.1441419

Year 2024, Volume: 73 Issue: 2, 336 - 348, 21.06.2024

Arzu Ece Çetin , Nursel Koyuncu

https://doi.org/10.31801/cfsuasmas.1373759

Abstract

References

  • Ali, N., Ahmad, I., Hanif, M., Shahzad, U., Robust-regression-type estimators for improving mean estimation of sensitive variables by using auxiliary information, Communications in Statistics-Theory and Methods, 3 (2019), 385–390. https://doi.org/10.1080/03610926.2019.1645857
  • Bouza, C. N., Ranked set sampling for the product estimator, Rev. Invest. Oper, 29(3) (2008), 201–206.
  • Koyuncu, N., Regression estimators in ranked set, median ranked set and neoteric ranked set sampling, Pakistan Journal of Statistics and Operation Research, 14(1) (2018), 89–94. https://doi.org/10.18187/pjsor.v14i1.1825
  • Koyuncu, N., Al-Omari, A. I., Generalized robust-regression-type estimators under different ranked set sampling, Mathematical Sciences, (2020). https://doi.org/10.1007/s40096-020-00360-7
  • Long, C., Chen, W., Yang, R., Yao D., Ratio estimation of the population mean using auxiliary under the optimal sampling design, Probability in the Engineering and Informational Sciences, 3 (2022), 449–460. https://doi.org/10.1017/s0269964820000625
  • Mclntyre, G. A., A method for unbiased selective sampling, using ranked sets, Australian Journal of Agricultural Research, 3 (1952), 385–390. https://doi.org/10.1071/ar9520385
  • Mehta, N., Mandowara, V. A., A modified ratio-cum-product estimator of finite population mean using ranked set sampling, Communication in Statistics- Theory and Methods, 45(2) (2016), 267–276. https://doi.org/10.1080/03610926.2013.830748
  • Muttlak, H. A., Investigating the use of quartile ranked set samples for estimating the population mean, Applied Mathematics and Computation, 146 (2003), 437–443. https://doi.org/10.1016/s0096-3003(02)00595-7
  • Samawi, H. M., Muttlak, H. A., Estimation of ratio using rank set sampling, Biometrical Journal, 38 (1996), 753-764. https://doi.org/10.1002/bimj.4710380616
  • Samawi, H. M., Ahmed, M. S.,Abu-Dayyeh, W., Estimating the population mean using extreme ranked set sampling, Biometrical Journal, 38(5) (1996), 577–586. https://doi.org/10.1002/bimj.4710380506
  • Shahzad, U., Hanif, M., Koyuncu, N., Luengo, A. V. G., A regression type estimator for mean estimation under ranked set sampling alongside the sensitivity issue, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2) (2019), 2037–2049. https://doi.org/10.31801/cfsuasmas.586057
  • Shahzad, U., Al-Noor, N., H., Hanif, M., Sajjad, I., Muhammad, A. M., Imputation based mean estimators in case of missing data utilizing robust regression and variance–covariance matrices, Communications in Statistics-Simulation and Computation, (2020), 1–20. https://doi.org/10.1080/03610918.2020.1740266
  • Subzar, M., Bouza, C. N., Al-Omari, A. I., Utilization of different robust regression techniques for estimation of finite population mean in srswor in case of presence of outliers through ratio method of estimation, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 40(5) (2019), 600–609. https://doi.org/10.32604/cmc.2020.010230
  • Zaman, T., Bulut, H., Modified ratio estimators using robust regression methods, Communications in Statistics-Theory and Methods, 48(8) (2019), 2019–2048. https://doi.org/10.1080/03610926.2018.1441419
There are 14 citations in total.

Details

Primary Language English
Subjects Theory of Sampling
Journal Section Research Articles
Authors

Arzu Ece Çetin 0000-0001-7224-9698

Nursel Koyuncu 0000-0003-1065-3411

Publication Date June 21, 2024
Submission Date October 10, 2023
Acceptance Date December 13, 2023
Published in Issue Year 2024 Volume: 73 Issue: 2

Cite

APA Çetin, A. E., & Koyuncu, N. (2024). Robust regression type estimators for body mass index under extreme ranked set and quartile ranked set sampling. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 73(2), 336-348. https://doi.org/10.31801/cfsuasmas.1373759
AMA Çetin AE, Koyuncu N. Robust regression type estimators for body mass index under extreme ranked set and quartile ranked set sampling. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2024;73(2):336-348. doi:10.31801/cfsuasmas.1373759
Chicago Çetin, Arzu Ece, and Nursel Koyuncu. “Robust Regression Type Estimators for Body Mass Index under Extreme Ranked Set and Quartile Ranked Set Sampling”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73, no. 2 (June 2024): 336-48. https://doi.org/10.31801/cfsuasmas.1373759.
EndNote Çetin AE, Koyuncu N (June 1, 2024) Robust regression type estimators for body mass index under extreme ranked set and quartile ranked set sampling. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73 2 336–348.
IEEE A. E. Çetin and N. Koyuncu, “Robust regression type estimators for body mass index under extreme ranked set and quartile ranked set sampling”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 73, no. 2, pp. 336–348, 2024, doi: 10.31801/cfsuasmas.1373759.
ISNAD Çetin, Arzu Ece - Koyuncu, Nursel. “Robust Regression Type Estimators for Body Mass Index under Extreme Ranked Set and Quartile Ranked Set Sampling”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73/2 (June 2024), 336-348. https://doi.org/10.31801/cfsuasmas.1373759.
JAMA Çetin AE, Koyuncu N. Robust regression type estimators for body mass index under extreme ranked set and quartile ranked set sampling. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2024;73:336–348.
MLA Çetin, Arzu Ece and Nursel Koyuncu. “Robust Regression Type Estimators for Body Mass Index under Extreme Ranked Set and Quartile Ranked Set Sampling”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 73, no. 2, 2024, pp. 336-48, doi:10.31801/cfsuasmas.1373759.
Vancouver Çetin AE, Koyuncu N. Robust regression type estimators for body mass index under extreme ranked set and quartile ranked set sampling. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2024;73(2):336-48.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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