An improved and robust class of variance estimator

Document Type : Article

Authors

1 Department of Statistics, Government College University, Faisalabad, 38000, Pakistan

2 College of Statistical and Actuarial Sciences, University of the Punjab Lahore, Pakistan

3 Department of Statistics, University of Sargodha, Sargodha, Pakistan

4 Department of Mathematics and Statistics, King Fahad University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

Abstract

The ratio, product, and regression estimators are commonly constructed based on the conventional measures such as mean, median, quartiles, semi-interquartile range, semi-interquartile average, coefficient of skewness, and coefficient of kurtosis. In case of the presence of outliers, these conventional measures lose their efficiency/performance ability and hence are of less efficient as compared to those measures which performed efficiently in the presence of outliers. This study offers improved class of estimators for estimating the population variance using robust dispersion measures such as probability-weighted moments, Gini’s, Downton’s and Bickel and Lehmann measures of an auxiliary variable. Bias, Mean square error (MSE) and minimum MSE of the suggested class of estimators have been derived. Application with two natural data sets is also provided to explain the proposal for practical considerations. In addition, a robustness study is also carried out to evaluate the performance of the proposed estimators in the presence of outliers by using an environment protection data. The results reveal that the proposed estimators perform better than its competitors and are robust, not only in simple conditions but also in the presence of outliers.

Keywords

References

References:
1. Solanki, R.S., Singh, H.P., and Pal, S.K. "Improved ratio-type estimators of finite population variance using quartiles", Hacettepe Journal of Mathematics and Statistics, 44(3), pp. 747-754 (2015).
2. Cochran, W.G., Sampling Techniques, 3rd Edn., John Wiley and Sons, New York (1977).
3. Isaki, C.T. "Variance estimation using auxiliary information", Journal of the American Statistical Association, 78, pp. 117-123 (1983).
4. Upadhyaya, L.N. and Singh., H.P. "An estimator for population variance that utilizes the kurtosis of an auxiliary variable in sample surveys", Vikram Mathematical Journal, 19, pp. 14-17 (1999).
5. Kadilar, C. and Cingi, H. "Ratio estimators for population variance in simple and stratified sampling", Applied Mathematics and Computation, 173, pp. 1047- 1058 (2006).
6. Subramani, J. and Kumarapandiyan, G. "Variance estimation using median of the auxiliary variable", International Journal of Probability and Statistics, 1(3), pp. 36-40 (2012).
7. 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).
8. Subramani, J. and Kumarapandiyan, G. "Estimation of variance using deciles of an auxiliary variable", Proceedings of International Conference on Frontiers of Statistics and Its Applications, 33, pp. 143-149 (2012).
9. Subramani, J. and Kumarapandiyan, G. "Estimation of variance using known coefficient of variation and median of an auxiliary variable", Journal of Modern Applied Statistical Methods, 12(1), pp. 58-64 (2013).
10. Khan, M. and Shabbir, J. "A ratio type estimators for the estimation of population variance using quartiles of an auxiliary variable", Journal of Statistics Applications and Probability, 2(3), pp. 319-325 (2013).
11. Hussain, Z. and Shabbir, J. "Estimation of the mean of a socially undesirable characteristics", Scientia Iranica, 20(3), pp. 839-845 (2013).
12. Zamanzade, E. and Vock, M. "Variance estimation in ranked set sampling using a concomitant variable", Statistics and Probability Letters, 105, pp. 1-5 (2015).
13. Yaqub, M. and Shabbir, J. "An improved class of estimators for finite population variance", Hacettepe Journal of Mathematics and Statistics, 45(5), pp. 1641-1660 (2016).
14. Abid, M., Abbas, N., and Riaz, M. "Improved modified ratio estimators of population mean based on deciles", Chiang Mai Journal of Science, 43(1), pp. 11311-1323 (2016).
15. Maqbool, S. and Javaid, S. "Variance estimation using linear combination of tri-mean and quartile average", American Journal of Biological and Environmental Statistics, 3(1), p. 5 (2017).
16. Adichwal, N.K., Sharma, P., and Singh, R. "Generalized class of estimators for population variance using information on two auxiliary variables", International Journal of Applied and Computational Mathematics, 3(2), pp. 651-661 (2017).
17. Maji, R., Singh, G.N., and Bandyopadhyay, A. "Effective estimation strategy of finite population variance using multi-auxiliary variables in double sampling", Journal of Modern Applied Statistical Methods, 16(1), pp. 158-178 (2017).
18. Zamanzade, E. and Wang, X. "Estimation of population proportion for judgment post-stratification", Computational Statistics and Data Analysis, 112, pp. 257-269 (2017).
19. Zamanzade, E. and Mahdizadeh, M. "A more efficient proportion estimator in ranked set sampling", Statistics and Probability Letters, 129, pp. 28-33 (2017).
20. 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 (2018).
21. Zamanzade, E. and Wang, X. "Proportion estimation in ranked set sampling in the presence of tie information", Computational Statistics, 33(3), pp. 1349-1366 (2018).
22. Hussain, S., Song, L., Ahmad, S., and Riaz, M. "On auxiliary information based improved EWMA median control charts", Scientia Iranica, 25(2), pp. 954-982 (2018).
23. Muneer, S., Khalil, A., Shabbir, J., and Narjis, G. "A new improved ratio-product type exponential estimator of finite population variance using auxiliary information", Journal of Statistical Computation and Simulation, 88(16), pp. 3179-3192 (2018).
24. Mahdizadeh, M. and Zamanzade, E. "Efficient body fat estimation using multistage pair ranked set sampling", Statistical Methods in Medical Research, 28(1), pp. 223-234 (2019).
25. Abid, M., Ahmed, S., Tahir, M., Nazir, H.Z., and Riaz, M. "Improved ratio estimators of variance based on robust measures", Scientia Iranica, 26(4), pp. 2484- 2494 (2019).
26. Abid, M., Abbas, N., Sherwani, R.A.K., and Nazir, Z.A. "Improved ratio estimators for the population mean using non-conventional measures of dispersion", Pakistan Journal of Statistics and Operation Research, 12(2), pp. 353-367 (2016).
27. Naz, F., Abid, M., Nawaz, T., and Pang, T. "Enhancing the efficiency of the ratio-type estimators of population variance with a blend of information on robust location measures", Scientia Iranic, 27, pp. 2040-2056 (2020).
28. Muhammad, F. and Riaz, M. "Probability weighted moments approach to quality control charts", Economic Quality Control, 21, pp. 251-260 (2006).
29. Gini, C. "Variabilita e mutabilita, contributo allo studio delle distribuzioni e delle relazioni statistiche", Studi Economico-Giuridici della R. Universita di Cagliari, 3, pp. 153-159 (1912).
30. Downton, F. "Linear estimates with polynomial coefficients", Biometrika, 53, pp. 129-141 (1966).
31. Bickel, P.J. and Lehmann, E.L. "Descriptive statistics for nonparametric models III: dispersion", In Contributions to Statistics, Hajek Memorial Volume, J.Jurekova, Ed., Academia, Prague, pp. 33-40 (1979).
32. David, H.A. "Gini's mean difference rediscovered", Biometrika, 55, pp. 573-575 (1968).
33. Shamos, M.I. "Geometry and statistics: problems at the interface", In New York Directions and Recent Results in Algorithms and Complexity, J.F. Traub, Ed., Academic Press, New York, pp. 251-280 (1976).
34. Murthy, M.N., Sampling Theory and Methods, Statistical Publishing Society, Calcutta, India (1967).
35. ISPRA. (2004). http://www.isprambiente.gov.it/en /databases.
Scientia Iranica
Volume 28, Issue 6 - Serial Number 6
Transactions on Industrial Engineering (E)
November and December 2021
Pages 3589-3601

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History

  • Receive Date: 22 February 2019
  • Revise Date: 11 December 2019
  • Accept Date: 21 September 2020

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