Generalized Variance Estimator using Auxiliary Information in the Presence and Absence of Measurement Error

Document Type : Research Note

Authors

Department of Statistics, National College of Business, Administration and Economics, Lahore, Pakistan

Abstract

In this study, we have proposed a new generalized estimator using auxiliary information for the estimation of population variance in presence and absence of measurement error. The expressions approximate bias and mean square error of the proposed generalized estimator are derive up to the first-order. Several new and existing estimators are found as the special cases of proposed estimator and expressed on various values of optimizing and generalized constants. The proposed estimator is compared mathematically with some existing estimators under certain conditions. The performance of proposed estimator is observed by simulation and real data application under different sample sizes. It is observed that the proposed estimator performed well than other competing estimators in the presence and absence of measurement error.

Keywords

References

References:
1. Isaki, C.T. "Variance estimation using auxiliary information", Journal of the American Statistical Association, 78(381), pp. 117-123 (1983). https://doi.org/10.1080/01621459.1983.10477939.
2. Kadilar, C. and Cingi, H. "Ratio estimators for the population variance in simple and stratified random sampling", Applied Mathematics and Computation, 173(2), pp. 1047-1059 (2006).https://doi.org/10.1016/j.amc.2005.04.032.
3. Shabbir, J. and Gupta, S.A.T. "On improvement in variance estimation", Communications in Statistics- Theory and Methods, 36(12), pp. 2177-2185 (2007).https://doi.org/10.1080/03610920701215092.
4. Singh, R., Chauhan, P., Sawan, N., et al. "Improved exponential estimator for population variance using two auxiliary variables", Italian Journal of Pure and Applied Mathematics, 28, pp. 101-108 (2011).
5. Yadav, S.K., Mishra, S.S., and Gupta, S. "An efficient estimator for population variance using parameters of an auxiliary variable", Journal of Statistics and Management Systems, 22(6), pp. 1005-1013 (2019a).https://doi.org/10.1080/09720510.2017.1406643.
6. Adichwal, N.K., Kumar, J., and Singh, R. "An improved generalized class of estimators for population variance using auxiliary variables", Cogent Mathematics and Statistics, 5(1), pp. 1-8 (2018). https://doi.org/10.1080/25742558.2018.1454579.
7. Singh, H.P., Pal, S.K., and Yadav, A. "A study on the chain ratio-ratio-type exponential estimator for finite population variance", Communications in Statistics - Theory and Methods, 47(6), pp. 1442-1458 (2017).https://doi.org/10.1080/03610926.2017.1321124.
8. Ismail, M., Kanwal, N., and Shahbaz, M.Q. "Generalized ratio-product-type estimator for variance using auxiliary information in simple random sampling", Kuwait Journal of Science, 45(1), pp. 79-88 (2018).
9. Bhat, M.A. "An improvement in variance estimator for the estimation of population variance, using known values of auxiliary information", International Journal of Pure and Applied Bioscience, 6(5), pp. 135-138 (2018). https://doi.org/10.18782/2320-7051.6842.
10. Javed, K., Jamal, N., Hanif, M., et al. "Improved estimator of finite population variance using coefficient of quartile deviation", Asian Journal of Advanced Research and Reports, 1(3), pp. 1-6 (2018). https://doi.org/10.9734/ajarr/2018/v1i313065.
11. Yadav, S.K., Sharma, D.K., and Mishra, S.S. "Searching efficient estimator of population variance using tri-mean and third quartile of auxiliary variable", International Journal of Business and Data Analytics, 1(1), pp. 30-40 (2019b). https://doi.org/10.1504/ijbda.2019.098830.
12. Hansen, M.H., Hurwitz, W.N., Marks, E.S., et al. "Response Errors in Survey", JASA, 46, pp. 147 - 190 (1951).
13. Singh, H.P. and Karpe, N. "A class of estimators using auxiliary information for estimating finite population variance in presence of measurement errors", Communications in Statistics - Theory and Methods, 38(5), pp. 734-741 (2009a). https://doi.org/10.1080/03610920802290713.
14. Misra, S., Yadav, D.K., Dipika, A., et al. "On estimation of population coefficient of variation in presence of measurement errors", International Journal of Mathematics Trends and Technology, 51(4), pp. 307- 311 (2017). https://doi.org/10.14445/22315373/ijmttv51p540.
15. Khalil, S., Noor-ul-Amin, M., and Hanif, M. "Estimation of population mean for a sensitive variable in the presence of measurement error", Journal of Statistics and Management Systems, 21(1), pp. 81-91 (2018). https://doi.org/10.1080/09720510.2017.1367478.
16. Zahid, E. and Shabbir, J. "Estimation of finite population mean for a sensitive variable using dual auxiliary information in the presence of measurement errors", PLoS ONE, 14(2), pp. 1-17 (2019). https://doi.org/10.1371/journal.pone.0212111.
17. Khalil, S., Gupta, S., and Hanif, M. "Estimation of finite population mean in stratified sampling using scrambled responses in the presence of measurement errors", Communications in Statistics -Theory and Methods, 48(6), pp. 1553-1561 (2019).
https://doi.org/10.1080/03610926.2018.1435817.
18. Du Nguyen, H. and Phuc Tran, K. "Effect of the measurement errors on two one-sided Shewhart control charts for monitoring the ratio of two normal variables", Quality and Reliability Engineering International, 36(5), pp. 1731-1750 (2020). https://doi.org/10.1002/qre.2656.
19. Singh, R., Bouza, C., and Mishra, M. "Estimation in stratified random sampling in the presence of errors", Revista Investigacion Operacional, 41(1), pp. 123-135 (2020).
20. Singh, H.P. and Karpe, N. "Estimation of population variance using auxiliary information in the presence of measurement errors", Statistics in Transition, 9(3), pp. 443-470 (2008).
21. Diana, G. and Giordan, M. "Finite population variance estimation in presence of measurement errors", Communications in Statistics - Theory and Methods, 41(23), pp. 4302-4314 (2012). https://doi.org/10.1080/03610926.2011.573165.
22. Sharma, P. and Singh, R. "A generalized class of estimators for finite population variance in presence of measurement errors", Journal of Modern Applied Statistical Methods, 12(2), pp. 231-241 (2013). https://doi.org/10.22237/jmasm/1383279120.
23. Singh, H.P. and Pal, S.K. "Improved estimation of finite population variance using auxiliary information in presence of measurement errors", Investigacion Operacional, 37(2), pp. 147-162 (2016).
24. Misra, S., Kumari, D., and Yadav, D.K. "Some improved estimators for estimating population variance in the presence of measurement errors", Journal of Statistics Applications and Probability, 5(2), pp. 311- 320 (2016). https://doi.org/10.18576/jsap/050212.
25. Masood, S. and Shabbirz, 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). https://doi.org/10.15672/HJMS.201612116352.
26. Singh, H.P. and Karpe, N. "A general procedure for estimating the general parameter using auxiliary information in presence of measurement errors", Communications for Statistical Applications and Methods, 16(5), pp. 821-840 (2009b). https://doi.org/10.5351/ckss.2009.16.5.821.
27. R Core Team., R: A language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria (2020). https://www.Rproject.org/.
28. Gujarati, D.N., Basic Econometrics (Fourth Ed., The McGraw-Hill Companies (2004).
29. Subramani, J. and Kumarapandiyan, G. "Variance estimation using quartiles and their functions of an auxiliary variable", International Journal of Statistics and Applications, 2(5), pp. 67-72 (2012). https://doi.org/10.5923/j.statistics.20120205.04.
30. Singh, R. and Malik, S. "Improved estimation of population variance using information on auxiliary attribute in simple random sampling", Applied Mathematics and Computation, 235, pp. 43-49 (2014). https://doi.org/10.1016/j.amc.2014.03.002.
31. Swain, A. "Generalized estimator of finite population variance", J Stat Theory Appl., 14(1), pp. 45-51 (2015).
32. Muili, J.O., Audu, A., Singh, R.V.K., et al. "Improved variance estimator using linear combination of tri-mean and quartile average", Annals. Computer Science Series, XVII(1), pp. 142-147 (2019).
Scientia Iranica
Volume 29, Issue 4
Transactions on Mechanical Engineering (B)
July and August 2022
Pages 1868-1879

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History

  • Receive Date: 14 December 2020
  • Revise Date: 24 November 2021
  • Accept Date: 25 April 2022

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