Efficient Method of Estimating the Finite Population Mean Based on Two Auxiliary Variables in the Presence of Non-Response Under Stratified Sampling
DOI:
https://doi.org/10.13052/jrss0974-8024.14111Keywords:
Study variable, auxiliary variable, finite population, non-response, bias, mean squared errorAbstract
This article addresses the problem of estimating the population mean using information on two auxiliary variables in presence of non-response on study variable only under stratified random sampling. A class of estimators has been defined. We have derived the bias and mean squared error up to first order of approximation. Optimum conditions are obtained in which the suggested class of estimators has minimum mean squared error. In addition to Chaudhury et al. (2009) estimator, many estimators can be identified as a member of the suggested class of estimators. It has been shown that the suggested class of estimators is better than the Chaudhury et al. (2009) estimator and other estimators. Results of the present study are supported through numerical illustration.
Downloads
References
Chaudhury, M. K., Singh, R., Shukla, R. K., Kumar, M. and Smarandache, F. (2009). A family of estimators for estimating population mean in stratified sampling under non-response, Pakistan Journal of Statistics and Operation Research, 5(1), 47–54.
Chaudhury, M. K., Singh, V. K., Singh, R., and Smarandache, F. (2011). Estimating the population mean in stratified population using auxiliary information under non-response. Studies in Sampling Techniques and Time Series Analysis, Zip Publishing, USA.
Cochran, W. G. (1977). Sampling techniques, 3rd Edition, John Wiley: New York.
Hansen, M. H. and Hurwitz, W. N. (1946). The problem of non-response in sample surveys, Journal of the American Statistical Association, 41, 517–529.
Haq, A. and Shabbir, J. (2013). Improved family of ratio estimators in simple and stratified random sampling, Communications in Statistics- Theory and Methods, 42(5), 782–799.
Khare, B. B. and Srivastava, S. (1993). Estimation of population mean using auxiliary character in presence of non-response, National Academy Science Letters, 16, 111–114.
Khare, B. B. and Srivastava, S. (1997). Transformed ratio-type estimators for the population mean in the presence of non-response, Communications in Statistics-Theory and Methods, 26(7), 1779–1791.
Khare, B. B., Srivastava, U. and Kamlesh, K. (2013). Generalized chain type estimators for ratio of two population means using two auxiliary characters in the presence of non-response, International Journal of Statistics and Economics, 10(1).
Koyuncu, N. and Kadilar, C. (2009). Ratio and product estimators in stratified random sampling, Journal of Statistical Planning and Inference, 139, 2552–2558.
Okafor F. C. and Lee, H. (2000). Double sampling for ratio and regression estimation with sub-sampling the non-respondent, Survey Methodology, 26(2), 183–188.
Rao, P. S. R. S. (1986). Ratio estimation with sub-sampling the non-respondents, Survey Methodology, 12(2), 217–230.
Saleem, I., Sanaullah, A. and Hanif, M. (2018). A generalized class of estimators for estimating population mean in the presence of non-response, Journal of Statistical Theory and Applications, 17(4), 616–626.
Sanaullah, A., Noor-ul-Amin, M. and Hanif, M. (2015). Generalized exponential-type ratio-cum-ratio and product-cum-product estimators for population mean in the presence of non-response under stratified two-phase random sampling, Pakistan Journal of Statistics and Operation Research, 31(1), 71–94.
Singh, G. N. and Khalid, M. (2015). Exponential chain dual to ratio and regression type estimators of population mean in two-phase sampling, Statistica, 75(4), 379–389.
Singh, H. P. and Kumar, S. (2008). A general family of estimators of finite population ratio, product and mean using two-phase sampling scheme in presence of non-response, Journal of Statistical Theory and Practice, 2(4), 677–692.
Singh, H. P. and Kumar, S. (2009). A general procedure of estimating the population mean in the presence of non-response under double sampling using auxiliary information, SORT, 33(1), 71–84.
Singh, H. P., Kumar, S. and Kozak, M. (2010). Improved estimation of finite population mean using sub-sampling to deal with non-response in two-phase sampling scheme, Communications in statistics-Theory and Methods, 39(5), 791–802.
Sukhatme, P. V., Sukhatme, B. V., Sukhatme, S. and Asok , C. (1984). “Sampling theory and surveys with applications”, Towa State University Press, Ames.
Tabasum, R. and Khan, I. A. (2004). Double sampling for ratio estimation with non-response, Journal of Indian Society of Agricultural Statistics, 53(3), 300–306.
Tabasum, R. and Khan, I. A. (2006). Double sampling ratio estimator for population mean in presence of non-response. Assam Statistical Review, 20, 73–83.
Tripathi, T. P. and Khare, B. B. (1997). Estimation of mean vector in presence of non-response, Communications and Statistics-Theory and Methods, 26(9), 2255–2269.