Efficient Class of Combined Ratio Type Estimators for Estimating the Population Mean under Non-response

Zakir Hussain Wani¹ , S.E.H. Rizvi² , Manish Sharma³ , M. Iqbal Jeelani Bhat⁴

Section:Research Paper, Product Type: Journal-Paper
Vol.8 , Issue.6 , pp.1-6, Dec-2021

Online published on Dec 31, 2021

Copyright © Zakir Hussain Wani, S.E.H. Rizvi, Manish Sharma, M. Iqbal Jeelani Bhat . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this paper, we investigate the issue of non-response in two different instances for estimating the population mean in stratified random sampling. Case I occurs when non-response is observed on both the study variable Y and the auxiliary variable X, and the population mean ( ) of the auxiliary variable is known; case II occurs when non-response is observed on the study variable Y, information on the auxiliary variable X is obtained from all sample units, and the population mean ( ) of the auxiliary variable X is known. We propose a class of combined ratio-type estimators that utilize known values of population characteristics of auxiliary variable such as coefficient of variation, kurtosis, skewness, standard deviation, median, mid-range, and correlation coefficient. The properties of the proposed estimators are obtained up to the first order of approximation. It has been shown empirically that the proposed estimators perform better than the existing estimators in terms of mean square errors.

Key-Words / Index Term :
Ratio estimator, Auxiliary variable, Bias, Mean square error, Relative efficiency

References :
[1] S. Bahl, R.K. Tuteja, “Ratio and product type exponential estimators,” J. Inform. Optim. Sci.Vol.12, issue.1,pp.159-164,1991.
[2] M.K. Chaudhary, A. Kumar, “Estimating the population mean in stratified random sampling using two-phase sampling in the presence of non-response,” World Applied Sciences Journal, Vol.33,issue.6,pp.874-882. 2015.
[3] M.K. Chaudhary, R. Singh. R. K. Shukla, “M. Kumar, A family of estimators for estimating population mean in stratified sampling under non-response,” Pakistan Journal of Statistics and Operation Research, Vol.5, issue.1, pp.47-54,2009.
[4] M. K. Chaudhary, V. K. Singh, R. K. Shukla, “Combined-type family of estimators of population mean in stratified random sampling under non-response,” Journal of Reliability and Statistical Studies (JRSS), Vol.5,iisue.2,pp.133-142.2012.
[5] , L. K. Grover, P. Kaur, “Exponential ratio type estimators of population mean under non-response,” Open Journal of Statistics,Vol.4,issue.1,pp.97-110,2014.
[6] M. H. Hansen, W. N. Hurwitz, “The problem of non-response in sample surveys,” J. Amer. Statist. Assoc, Vol.41, issue.236, pp.517-529, 1946.
[7] M.G.M. Khan, E. A. Khan, M. J. Ahsan, “Optimum allocation in multivariate stratified sampling in the presence of non-response,” J. Ind. Soc. Agric. Statist, Vol.62, issue.1, pp.42-48, 2008.
[8] M. Khan, A. Y. Al-Hossain, “A note on a difference-type estimator for population mean under two-phase sampling design,” Springerplus, Vol.5, issue. 1, pp.723. 2016.
[9] B.B. Khare, S. Srivastava, “Transformed ratio type estimators for the population mean in the presence of non-response,” Comm. Statist. Theory Methods, Vol.26,issue.7,pp.1779-1791.1997.
[10] M. Kumar, R. Singh, N. Sawan, P. Chauhan, “Exponential ratio method of estimators in the presence of measurement errors,” International Journal of Agricultural and Statistical Sciences, Vol.7, issue.2, pp.457-461. 2011).
[11] M. N. Murthy, “Sampling theory and methods,” Calcutta, India: Statistical Publishing Society, 1967.
[12] R. Pandey, N. S. Thakur, K. Yadav, “Estimation of population mean using exponential ratio type imputation method under survey non-response,” J. Indian Statist. Assoc., Vol.53, issue.1-2, pp. 89-107.2015.
[13] A. Sanaullah, H. M. Ali, M. Noor-ul-Amin, M. Hanif, “Generalized exponential chain ratio estimators under stratified two-phase random sampling,” Applied Mathematics and Computation, Vol.226, pp.541–47. 2014.
[14] A. Sanaullah, M. Noor-ul-Amin, M Hanif, R. Singh, “Generalized exponential chain estimators using two auxiliary variables for stratified sampling with non-response,” Science International (Lahore), Vol.27, isssue 2, pp.901–15,2015.
[15] A. Sanaullah, M. Noor-ul-Amin, M. Hanif, N. Koyuncu, “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 and Computational Mathematics, Vol.4,issue.2,pp.1–28. 2018.
[16] P. Sharma, R. Singh, “A generalized class of estimator for population variance in presence of measurement errors,” Journal of Modern Applied Statistical Methods, Vol.12,issue.2,pp. 231-241.2013.
[17] R. Singh, P. Chauhan, N. Sawan, F. Smarandache, “Improvement in estimating the population mean using exponential estimator in simple random sampling,” Bull. Stat. Econ. Vol.3, issue.09, pp. 13-18,2009.
[18] S. R. Singh, P. Sharma, “Method of estimation in the presence of non-response and measurement errors simultaneously,” Journal of Modern Applied Statistical Methods, Vol.14, issue.1,pp. 107-121,2015.
[19] R. Tabasum, I.A. Khan, “Double sampling for ratio estimation with non-response,” Journal of the Indian Society of Agriculture Statistics, Vol.53, issue.3,pp.300–06,2004.
[20] C. Unal, C. Kadilar, “Exponential type estimator for the population mean in the presence of non-response,” Journal of Statistics and Management Systems 2019. doi: 10.1080/09720510.2019.1668158
[21] C. Unal, C. Kadilar, “A New Family of Exponential Type Estimators in the Presence of Non-Response,” J. Math. Fund. Sci, Vol.53, issue.1, pp.1-15, 2021.