Combined type generalized classes of efficient estimators of mean in joint presence of measurement error and non-response using stratified two-phase sampling

Document Type : Article

Authors

Department of Statistics, COMSATS University Islamabad, Lahore Campus, Pakistan

Abstract

In this study, three classes of generalized and more efficient combined regression-cum-ratio estimators are presented to estimate the population mean of the study variable in stratified two-phase sampling considering non-response and measurement error are present jointly. The expressions for the bias and mean square error of the three proposed generalized combined regression-cum-ratio estimators have been obtained. Optimal conditions which make the proposed generalized regression-cum-ratio estimators more efficient than modified combined regression estimator are discussed. The performance of the proposed generalized combined regression-cum-ratio estimators has been compared theoretically as well as empirically with various combined type estimators in stratified two-phase sampling including usual combined ratio estimator, usual combined exponential ratio estimator, usual combined regression estimator, and modified combined regression estimator. An empirical study shows that the proposed generalized combined regression-cum-ratio estimators perform more efficiently than all combined type ratio, exponential ratio, and regression estimators discussed in the study.

Keywords

References

References:
1. Sanaullah, A., Noor-ul-amin, M., and Hanif, M. "Generalized exponential-type ratio-cum-ratio and productcum- product estimators for population mean in the presence of non-response under stratified two-phase random sampling", Pakistan Journal of Statistics, 31(1), pp. 71-94 (2015).
2. Sanaullah, A., Noor-ul-amin, M., Hanif, M., et al. "Generalized exponential-type estimators for population mean taking two auxiliary variables for unknown means in stratified sampling with sub-sampling the non-respondents", International Journal of Applied Computational Mathematics, 4(56) (2018). DOI: 10.1007/s40819-018-0489-7.
3. Samiuddin, M. and Hanif, M. "Estimation of population mean in single and two phase sampling with or without additional information", Pakistan Journal of Statistics, 23(2), pp. 99-118 (2007).
4. Sanaullah, A., Noor-ul-amin, M., Hanif, M., et al. "Generalized exponential chain estimators using two auxiliary variables for stratified sampling with nonresponse", Science International, (Lahore) , 27(2), pp. 901-915 (2015).
5. Saleem, I., Sanaullah, A., and Hanif, M. "A generalized class of estimators for estimating populationmean in the presence of non-response", Journal of Statistical Theory and Applications, 17(4), pp. 616-626 (2018). DOI: 10.2991/jsta.2018.17.4.4.
6. Koyuncu, N. and Kadilar, C. "Family of estimators of population mean using two auxiliary variables in stratified random sampling", Communications in Statistics- Theory and Methods, 38(1), pp. 2398-2417 (2009). DOI: 10.1080/03610920802562723.
7. Saleem, I., Sanaullah, A., and Hanif, M. "Generalized family of estimators in stratified random sampling using sub-sampling of non-respondents", Journal of Reliability and Statistical Studies, 11(2), pp. 159-173 (2019).
8. Shabbir, J., Gupta, S., and Ahmed, S. "A generalized class of estimators under two-phase stratified sampling for non-response", Communication in Statistics- Theory and Methods, 48(15), pp. 3761-3777 (2019). DOI: 10.1080/03610926.2018.1481969.
9. Grover, L.K. and Kaur, P. "An improved estimator of the finite population mean in simple random sampling", Model Assisted Statistics and Application, 6(1), pp. 47-55 (2011). DOI: 10.3233/MAS-2011-0163.
10. Khare, B.B. and Jha, P.S. "Classes of estimators for population mean using auxiliary variable in stratified population in the presence of non response", Communications in Statistics-Theory and Methods, 46(13), pp. 6579-6589 (2017). DOI: 10.1080/03610926.2015.1130841.
11. Singh, G.N. and Usman, M. "Generalized class of estimators using dual of auxiliary variable under non response", Journal of Statistical Theory and Practice, 15(41) (2021). DOI: 10.1007/s42519-021-00184-1.
12. Unal, C. and Kadilar, C. "Improved family of estimators using exponential function for the population mean in the presence of non-response", Communications in Statistics-Theory and Methods, 50(1), pp. 237-248 (2021). DOI: 10.1080/03610926.2019.1634818.
13. Sanaullah, A. and Hanif, M. "Generalized chain exponential-type estimators under stratified two-phase sampling with sub-sampling the non-respondents", Journal of Statistical Theory and Applications, 19(2), pp. 185-195 (2020). DOI: 10.2991/jsta.d.200507.002.
14. Ehsan, I. and Sanaullah, A. "Generalized dual estimators for estimating mean using sub-sampling the non-respondents", Journal of Reliability and Statistical Studies, 12(1), pp. 139-158 (2019).
15. Sanaullah, A., Ehan, I., and Noor-ul-amin, M. "Estimation of mean for a finite population using subsampling of non-respondents", Journal of Statistics and Management System, 22(6), pp. 1015-1035 (2019). DOI: 10.1080/09720510.2019.1572981.
16. Wua, F., Wang, J., and Ma, Y. "Robust parameter design based on response surface model under considering measurement errors", Scientia Iranica, 28(4), pp. 2323-2332 (2019). DOI: 10.24200/sci.2019.50622.1793.
17. Varshney, R. and Mradula. "Optimum allocation in multivariate stratified sampling design in the presence of nonresponse with Gamma cost function", Journal of Statistical Computation and Simulation, 89(13), pp. 2454-2467 (2019). DOI: 10.1080/00949655.2019.1620747.
18. Cochran, W.G., Sampling Techniques, 3rd Ed., New York: John Wiley and Sons, Inc. (1977). 
19. Singh, H.P. and Karpe, N. "Estimation of mean, ratio and product using auxiliary information in the presence of measurement errors in sample surveys", Journal of Statistical Theory and Practice, 4(1), pp. 111- 136 (2010). DOI: 10.1080/15598608.2010.10411976.
20. Shukla, D., Pathak, S., and Thakur, N.S. "An estimator for mean estimation in presence of measurement error", Research and Review: Journal of Statistics, 1(1), pp. 1-8 (2012).
21. Manisha and Singh, R.K. "An estimation of population mean in the presence of measurement errors", Journal of Indian Society of Agricultural Statistics, 54(1), pp. 13-18 (2001). 
22. Masood, S. and Shabbir, J. "Generalized multiphase regression-type estimators under the effect of measurement error to estimate the population variance", Hacettepe Journal of Mathematics and Statistics, 45(4), pp. 1297-1306 (2016). DOI: 10.15672/HJMS.201612116352.
23. Khalil, S., Gupta, S., and Hanif, M. "A generalized estimator for finite population mean in the presence of measurement errors in stratified sampling", Journal of Statistical Theory and Practice, 12(2), pp. 311-324 (2018). DOI: 10.1080/15598608.2017.1370621.
24. Shalabh, and Tsai, Jia-Ren. "Ratio and product methods of estimation of population mean in the presence of correlated measurement errors", Communications in Statistics-Simulation and Computation, 46(7), pp. 5566-5593 (2017). DOI: 10.1080/03610918.2016.1165845.
25. Khalil, S., Noor-ul-amin, M., and Hanif, M. "Generalized estimator of population mean by using conventional and non-conventional measures in the presence of measurement errors", Communications in Statistics- Simulation and Computation, 48(2), pp. 516-529 (2019). DOI: 10.1080/03610918.2017.1387662.
26. Singh, N., Vishwakarma, G.K., and Kim, J.M. "Computing the effect of measurement errors on efficient variant of the product and ratio estimators of mean using auxiliary information", Communications in Statistics-Simulation and Computation, 51(2), pp. 604-625 (2019). DOI: 10.1080/03610918.2019.1656742.
27. Yaqub, M. and Shabbir, J. "Estimation of population distribution function involving measurement error in the presence of non response", Communications in Statistics-Theory and Methods, 49(10), pp. 2540-2559 (2020). DOI: 10.1080/03610926.2019.1580738.
28. Singh, G.N., Bhattacharyya, D., and Bandyopadhyay, A. "Some logarithmic and sine-type imputation techniques for missing data in survey sampling in the presence of measurement errors", Journal of Statistical Computation and Simulation, 91(4), pp. 713-731 (2021). DOI: 10.1080/00949655.2020.1828414.
29. Azeem, M. "On estimation of population mean in the presence of measurement error and non-response", Unpublished PhD thesis, National College of Business Administration and Economics, Lahore, Pakistan (2014).
30. Kumar, S., Bhougal, S., and Nataraja, N.S. "Estimation of population mean in the presence of nonresponse and measurement error", Revista Colombiana de Estadstica, 38(1), pp. 145-161 (2015). DOI: 10.15446/rce.v38n1.48807.
31. Kumar, S. "Improved estimation of population mean in presence of non-response and measurement error", Journal of Statistical Theory and Practice, 10(4), pp. 707-720 (2016). DOI: 10.1080/15598608.2016.1216488.
32. Azeem, M. and Hanif, M. "Joint influence of measurement error and non-response on estimation of population mean", Communications in Statistics-Theory and Methods, 46(4), pp. 1679-1693 (2017). DOI: 10.1080/03610926.2015.1026992.
33. Irfan, M., Javed, M., and Lin, Z. "Optimized estimation for population mean using conventional and non-conventional measures under the joint influence of measurement error and nonresponse", Journal of Statistical Computation and (2018). DOI: 10.1080/00949655.2018.1464571.
34. Sabir, S. and Sanaullah, A. "A note on Kumar (2016): Improved estimation of population mean in the presence of measurement error and non-response", Journal of Statistical Theory and Practice, 13(25) pp. 1-5 (2019). DOI: 10.1007/s42519-018-0025-4.
35. Zahid, E. and Shabbir, J. "Estimation of population mean in the presence of measurement error and nonresponse under stratified random sampling", PLOS ONE, 13(2): e0191572 (2018). DOI: 10.1371/journal. pone.0191572.
36. Kumar, S., Trehan, M., and Joorel, S.P.J. "A simulation study: Estimation of population mean using two auxiliary variables in stratified random sampling", Journal of Statistical Computation and Simulation, 88(18), pp. 3694-3707 (2018). DOI: 10.1080/00949655.2018.1532513.
37. Hansen, M.H. and Hurwitz, W.N. "The problem of non-response in sample surveys", Journal of American Statistical Association, 41, pp. 517-529 (1946). DOI: 10.1080/01621459.1946.10501894.
38. Zamanzade, E. and Mahdizadeh, M. "A more efficient proportion estimator in ranked set sampling", Statistics and Probability Letters, 129, pp. 28-33 (2017). DOI: 10.1016/j.spl.2017.05.001.
39. Zamanzade, E. and Wang, X. "Estimation of population proportion for judgment post-stratification", Computational Statistics and Data Analysis, 112, pp. 257-269 (2017). DOI: 10.1016/j.csda.2017.03.016.
40. Dumbgen, L. and Zamanzade, E. "Inference on a distribution function from ranked set samples", Annals of the Institute of Statistical Mathematics, 72(1), pp. 157-185 (2020). DOI: 10.1007/s10463-018-0680-y.
Scientia Iranica
Volume 31, Issue 18
Transactions on Industrial Engineering (E)
November and December 2024
Pages 1567-1595

Files

Share

How to cite

Statistics