Improved Estimators For The Population Mean Under Non-Response

Year 2023, Volume: 36 Issue: 2, 920 - 931, 01.06.2023

Khalid Ul İslam Rather , Cem Kadılar

https://doi.org/10.35378/gujs.933452

Abstract

We propose a novel family of estimators for the population mean under non-response and obtain the MSE equation of the suggested estimator for each situation in theory. These theoretical conditions are applied to three popular data sets in literature and we see that the suggested estimators are more efficient than the traditional estimators, such as ratio, regression estimators, in Case 1; whereas, in Case 2, the suggested estimators are also more efficient than the Unal-Kadilar exponential estimators that are more efficient than the traditional estimators for the same data sets. 

Keywords

Exponential Type, Estimators, Non-Response, Mean Squared Error, Efficiency

References

• [1] Cochran, W. G., “The estimation of the yields of the cereal experiments by sampling for the ratio of grain to total produce”, The Journal of Agricultural Science, 30(2): 262-275, (1940).
• [2] Cochran, W. G., “Sampling Techniques”, Third Edition, John Wiley and Sons, New-York, 448, (1977).
• [3] Bahl, S., Tuteja, R. K., “Ratio and product type exponential estimators”, Journal of Information and Optimization Sciences, 12(1): 159-164, (1991).
• [4] Yadav, S.K., Kadilar, C., “Efficient family of exponential estimators for the population mean”, Hacettepe Journal of Mathematics and Statistics, 42(6): 671-677, (2013).
• [5] Singh, H.P., Pal, S.K., “A new chain ratio-ratio-type exponential estimator using auxiliary information in sample surveys”, International Journal of Mathematics and its Applications, 3(4B): 37-46, (2015).
• [6] Hansen, M.H., Hurwitz, W.N., “The problem of non-response in sample surveys”, Journal of the American Statistical Association, 41(236): 517-529, (1946).
• [7] Rao, P. S. R. S., “Ratio estimation with sub sampling the non-respondents”, Survey Methodology, 12: 217–230, (1986).
• [8] Singh, R., Kumar, M., Chaudhary, M. K., Smarandache, F., “Estimation of mean in presence of non-response using exponential estimator”, arXiv preprint arXiv:0906.2462, (2009).
• [9] Unal, C., Kadilar, C., “Improved family of estimators using exponential function for the population mean in the presence of non-response”, Communications in Statistics-Theory and Methods, 50(1): 237-248, (2021).
• [10] Singh, H.P., Kumar, S., “A regression approach to the estimation of finite population mean in presence of non-response”, Australian and New Zealand Journal of Statistics, 50(4): 395-408, (2008).
• [11] Kumar, S., “Improved exponential estimator for estimating the population mean in the presence of non response”, Communications for Statistical Applications and Methods, 20(5): 357-366, (2013).
• [12] Pal, S. K., Singh, H. P., “Estimation of mean with two-parameter ratio-product-ratio estimator in double sampling using auxiliary information under non-response”, Journal of Modern Applied Statistical Methods, 17(2): 2–32, (2018).
• [13] Khare, B. B., Sinha, R. R., “Estimation of product of two population means by multiauxiliary characters under double sampling the non-respondents”, Statistics in Transition New Series, 20(3): 81–95, (2019).
• [14] Kumar, S., Sharma, V., “Improved chain ratio-product type estimators under double sampling scheme”, Journal of Statistics Applications and Probability Letters, 7(2): 87–96, (2020).
• [15] Sharma, V., Kumar, S., “Estimation of population mean using transformed auxiliary variable and non response”, Revista De Investigacion Operacional, 41(3): 438-444, (2020).
• [16] Irfan, M., Javed, M., Lin, Z., “Enhanced estimation of population mean in the presence of auxiliary information”, Journal of King Saud University, 31: 1373-1378, (2019).
• [17] Khare, B. B., Sinha, R. R., “On class of estimators for population mean using multi-auxiliary characters in the presence of non-response”, Statistics in Transition, 10(1): 3-14, (2009).
• [18] Khare, B. B., Srivastava, S., “Estimation of population mean using auxiliary character in presence of non-response”, National Academic Science Letters India, 16(3): 111-114, (1993).