Improved ratio estimators using some robust measures

Year 2018, Volume: 47 Issue: 5, 1375 - 1393, 16.10.2018

Muhammad Abid , Hafız Zafar Nazir , Muhammad Riaz , Zhengyan Lin Hafız Muhammad Tahir

https://izlik.org/JA69CS54AM

Abstract

Estimation of population mean is of prime concern in many studies and ratio estimators are popular choices for it. It is a common practice to use conventional measures of location to develop ratio estimators using information on auxiliary variables. In this article, we propose a class of ratio estimators for a finite population mean using information on two auxiliary variables with the help of some non-conventional location measures. We have incorporated tri-mean, Hodges-Lehmann, mid-range and decile mean of the two auxiliary variables to serve the purpose. The properties associated with the proposed class of ratio estimators are evaluated using mean square error. We have presented efficiency comparisons of the proposed class of ratio estimators with other existing estimators under the optimal conditions. An empirical study is also included for illustration and verication purposes. From theoretical and empirical study, We observed that the proposed estimators perform better as compared to the usual ratio and the existing estimators consider in this study.

Keywords

Auxiliary variables , Hodges-Lehmann estimator , Mean square error , Mid-range , Ratio estimators , Tri-mean

References

• Abid, M., Abbas, N., Nazir, H. Z. and Lin, Z. Enhancing the mean ratio estimators for es- timating population mean using non-conventional location parameters, Revista Colombiana de Estadistica 39 (1), 63-79, 2016(a).
• Abid, M., Abbas, N. and Riaz, M. Improved modified ratio estimators of population mean based on deciles, Chiang Mai Journal of Science 43 (1), 1311-1323, 2016(b).
• Abid, M., Abbas, N., Sherwani, R. A. K. and Nazir, H. Z. Improved ratio estimators for the population mean using non-conventional measures of dispersion, Pakistan Journal of Statistics and Operation Research 12 (2), 353-367, 2016(c).
• Abid, M., Sherwani, R. A. K., Abbas, N. and Ali, M. R. Some Improved modified ratio estimators based on dedile mean of an auxiliary variable, Pakistan Journal of Statistics and Operation Research 12 (4), 787-797, 2016.
• Abu-Dayeh, W.A., Ahmed, M.S., Ahmed, R.A. and Muttlak, H.A. Some estimators of a finite population mean using auxiliary information, Applied Mathematics and Computation 139, 287-298, 2003.
• Al-Hossain, A.Y., and Khan, M. Efficiency of ratio, product and regression estimators under maximum and minimum values, using two auxiliary variables, Journal of Applies Mathe- matics201, 1-6, 2014.
• Cochran, W. G. Sampling techniques (John Wiley and Sons, New-York,1977) .
• Ferrell, E.B. Control charts using midranges and medians, Industrial Quality Control 9, 30-34, 1953.
• Hettmansperger, T.P., and McKean, J. W. Robust nonparametric statistical methods (Arnold London, 1998).
• Kadilar, C., and Cingi, H. Ratio estimators in simple random sampling, Applied Mathe- matics and Computation 151, 893-902, 2004.
• Kadilar, C., and Cingi, H. Estimator of a population mean using two auxiliary variables in simple random sampling, International Mathematical Journal 5- 357-360, 2004.
• Kadilar, C., and Cingi, H. A new estimator using two auxiliary variables, Applied Mathe- matics and Computation 162, 901-908, 2005.
• Kadilar, C., and Cingi, H. An Improvement in estimating the population mean by using the correlation coefficient, Hacettepe Journal of Mathematics and Statistics 55 (1), 103-109, 2006.
• Khare, B. B., Srivastava, U., and Kumar, K. A generalized chain ratio in regression es- timator for population mean using two auxiliary characters in sample survey, Journal of Scientific Research 57, 147-153, 2013.
• Lu, J. The chain ratio estimator and regression estimator with linear combination of two auxiliary variables, PLOS ONE 11 (8) , 1-4, 2013.
• Lu, J., and Yan, Z. A class of ratio estimators of a finite population mean using two auxiliary variables, PLOS ONE 2 (9), 1-6, 2014.
• Lu, J., Yan, Z., and Peng X. A new exponential ratio type estimator with linear combination of two auxiliary variables, PLOS ONE, 12 (9), 1-10, 2014.
• Murthy, M. N. Sampling Theory and Methods (Statistical Publishing Society, Calcutta, India, 1967.)
• Olkin, I. Multivariate ratio estimation for finite populations, Biometrika 45, 154-165, 1958.
• Perri, P. F. Improved ratio-cum-product type estimators, Statistics in Transition 1 (8), 51-69, 2007.
• Raj, D. On a method of using multi-auxiliary information in sample surveys, Journal of the American Statistical Association 60, 154-165, 1965.
• Singh, D., and Chaudhary, F. S. Theory and analysis of sample survey designs (New Age International Publisher, New Delhi, India, 1986).
• Singh, G. N. On the improvement of product method of estimation in sample surveys, Journal of the Indian Society of Agricultural Statistics 56 (3), 267-265, 2003.
• Singh, H. P., and Tailor, R. Use of known correlation coefficient in estimating the finite population means, Statistics in Transition 6 (4), 555-560, 2003.
• Singh, H. P., and Tailor, R. Estimation of finite population mean using known correlation coefficient between auxiliary characters, Statistica 65, 407-418, 2005
• Sisodia, B. V. S., and Dwivedi, V. K. A modified ratio estimator using coefficient of variation of auxiliary variable, Journal of the Indian Society of Agricultural Statistics 33 (1), 13-18, 1981.
• Srivastava, S.K. A generalized estimator for the mean of a finite population using multiauxiliary information, Journal of American Statistical Association 66, 404-407, 1971.
• Srivastava, S.K., and Jhajj, H.S. A class of estimators of the population mean using multi- auxiliary information, Calcutta Statistical Association Bulletin 32, 47-56, 1983.
• Subramani, J., and Kumarapandiyan, G. Estimation of population mean using known me- dian and co-efficient of skewness, American Journal of Mathematics and Statistics 2 (5), 101-107, 2012.
• Subramani, J., and Kumarapandiyan, G. Estimation of population mean using co-effcient of variation and median of an auxiliary variable, International Journal of Probability and Statistics1 (4), 111-118, 2012.
• Subramani, J., and Kumarapandiyan, G. Modified ratio estimators using known median and co-efficient of kurtosis, American Journal of Mathematics and Statistics2 (4), 95-100, 2012.
• Subramani, J., and Kumarapandiyan, G. A class of modied ratio estimators using deciles of an auxiliary variable, International Journal of Statistical Applications 2, 101-107, 2012.
• Subramani, J., and Kumarapandiyan, G. A new modified ratio estimator for estimation of population mean when median of the auxiliary variable is known, Pakistan Journal of Statistics and Operation Research9 (2), 137-145, 2013.
• Subramani, J., and Prabavathy, G. Two parameters modified ratio estimators with two auxiliary variables for estimation of finite population mean with known skewness, kurtosis and correlation coefficient, Journal of Modern Applied Statistical Methods13 (1), 199-222, 2014.
• Upadhyaya, L. N., and Singh, H. P. Use of transformed auxiliary variable in estimating the finite population mean, Biometrical Journal 41 (5), 627-636, 1999.
• Wang, T., Li, Y., and Cui, H. On weighted randomly trimmed means, Journal of Systems Science and Complexity 20, 47-65, 2007.
• Yan, Z., and Tian, B. Ratio method to the mean estimation using coefficient of skewness of auxiliary variable, ICICA 2010, Part II, CCIS106, 103-110, 2010.