Improving Population Mean Accuracy through Optimal Estimator
Keywords:
Auxiliary information, Bias, Mean squared error, Non-response, Percentage relative efficiency, Ratio-product-cum-difference estimatorAbstract
In sample surveys, non-response is a common issue that reduces the accuracy and reliability of estimators of population parameters. To address this problem, auxiliary information is often utilized to improve estimation efficiency. In this paper, they propose a new family of transformed ratio–product–cum–difference (RPCD) estimators for estimating the finite population mean in the presence of non-response. The bias and mean squared error (MSE) expressions of the proposed estimators are derived up to the first order of approximation, and the optimum conditions for minimizing the MSE are established. The theoretical efficiency of the proposed estimators is compared with several existing estimators available in the literature. The results show that the proposed family performs better under certain parametric conditions and provides substantial gains in efficiency. An empirical study based on a natural population data set is conducted to validate the theoretical findings. The percentage relative efficiency (PRE) values demonstrate the superiority of the suggested estimators over the competing estimators. Therefore, the proposed family offers a flexible and efficient alternative for practical survey applications involving incomplete information.
References
M. H. Hansen and W. N. Hurwitz, “The problem of non-response in sample surveys,” Journal of the American Statistical Association, vol. 41, no. 236, pp. 517–529, Dec. 1946.
W. G. Cochran, Sampling Techniques. New York, NY, USA: John Wiley & Sons, 1977.
T. Srivenkataramana and D. S. Tracy, “Extending product method of estimation to positive correlation case in surveys,” Australian Journal of Statistics, vol. 23, no. 1, pp. 95–100, Mar. 1981.
P. S. R. S. Rao, “Ratio estimation with sub-sampling of the non-respondents,” Survey Methodology, vol. 12, no. 2, pp. 217–230, 1986.
B. B. Khare and S. Srivastava, “Transformed ratio type estimators for the population mean in the presence of nonresponse,” Communications in Statistics—Theory and Methods, vol. 26, no. 7, pp. 1779–1791, Jul. 1997.
F. C. Okafor and H. Lee, “Double sampling for ratio and regression estimation with sub-sampling of the non-respondents,” Survey Methodology, vol. 26, no. 2, pp. 183–188, Dec. 2000.
S. Kumar, H. P. Singh, E. Bhougal, and R. Gupta, “A class of ratio-cum-product type estimators under double sampling in the presence of non-response,” Hacettepe Journal of Mathematics and Statistics, vol. 40, no. 4, pp. 589–599, 2011.
O. Yunusa and S. Kumar, “Ratio-cum-product estimator using exponential estimator in the presence of non-response,” Journal of Advanced Computing, vol. 3, no. 1, pp. 1–11, 2014.
W. W. Chanu and B. K. Singh, “Improved exponential ratio cum exponential dual to ratio estimator of finite population mean in the presence of non-response,” Journal of Statistics Applications & Probability, vol. 4, no. 1, p. 103, Mar. 2015.
C. Kadılar and H. Cingi, “An improvement in estimating the population mean by using the correlation coefficient,” Hacettepe Journal of Mathematics and Statistics, vol. 35, no. 1, pp. 103–109, 2006.
S. Kumar, “Ratio cum regression estimator for estimating a population mean with a sub sampling of non respondents,” Communications for Statistical Applications and Methods, vol. 19, no. 5, pp. 663–671, 2012.
S. Kumar and M. Vishwanathaiah, “A generalized family of transformed estimators in the presence of non-response in sample surveys,” Journal of Advanced Computing, vol. 2, no. 3, pp. 99–109, 2013.
S. K. Pal and H. P. Singh, “Finite population mean estimation through a two-parameter ratio estimator using auxiliary information in presence of non-response,” Journal of Applied Mathematics, Statistics and Informatics, vol. 12, no. 2, pp. 5–39, Dec. 2016.
H. P. Singh and R. Tailor, “Use of known correlation coefficient in estimating the finite population mean,” Statistics in Transition, vol. 6, no. 4, pp. 555–560, 2003.
C. Unal and C. Kadilar, “A new population mean estimator under non-response cases,” Journal of Taibah University for Science, vol. 16, no. 1, pp. 111–119, Dec. 2022.
A. A. Ahmadini, T. Yadav, S. K. Yadav, and A. S. Al Luhayb, “Restructured Searls family of estimators of population mean in the presence of nonresponse,” Frontiers in Applied Mathematics and Statistics, vol. 8, Art. no. 969068, Oct. 2022.
S. Kumar and P. Chhaparwal, “Estimation of population mean in the presence of non-response for time-based surveys,” Thailand Statistician, vol. 23, no. 2, pp. 438–446, Mar. 2025.
A. Kumari, P. Sharma, and R. Singh, “Estimation of population mean using ranked set sampling in the presence of non-response error with numerical illustration and simulation study,” Quality & Quantity, pp. 1–27, Nov. 2025.
S. Kumar, C. Rani, H. P. Singh, and J. P. Joorel, “Efficient estimation method of population mean with non-response and observational error under ORRT models,” Research in Statistics, vol. 3, no. 1, Art. no. 2522734, Dec. 2025.
N. Dansawad, “A modified population mean estimator for sample surveys with nonresponse problems,” Mathematics and Statistics, vol. 13, no. 1, pp. 48–55, Feb. 2025.
C. Kadılar and H. Cıngı, “A study on the chain ratio-type estimator,” Hacettepe Journal of Mathematics and Statistics, vol. 32, no. 1, pp. 105–108, 2003.
A. K. Swain, “On an improved ratio type estimator of finite population mean in sample surveys,” Operations Research, vol. 35, no. 1, 2014.
A. Kumar, C. Singh, R. Agarwal, and V. K. Kashyap, “An improved estimation procedure for population mean in the presence of non-response,” Revista Colombiana de Estadística, vol. 49, no. 1, p. 307, 2026.
T. Srivenkataramana, “A dual to ratio estimator in sample surveys,” Biometrika, vol. 67, no. 1, pp. 199–204, Jan. 1980.
S. Bandyopadhyaya, “Improved ratio and product estimators,” Sankhya C, vol. 42, nos. 1–2, pp. 45–49, 1980.
B. V. Sisodia and V. K. Dwivedi, “A modified ratio estimator using the coefficient of variation of the auxiliary variable,” Journal of the Indian Society of Agricultural Statistics, vol. 33, no. 1, pp. 13–18, 1981.
A. Sahai and A. Sahai, “On efficient use of auxiliary information,” Journal of Statistical Planning and Inference, vol. 12, pp. 203–212, Jan. 1985.
L. N. Upadhyaya and H. P. Singh, “Use of transformed auxiliary variable in estimating the finite population mean,” Biometrical Journal, vol. 41, no. 5, pp. 627–636, Sep. 1999.
B. B. Khare and R. R. Sinha, “Estimation of finite population ratio using a two-phase sampling scheme in the presence of non-response,” Aligarh Journal of Statistics, vol. 24, pp. 43–56, 2004.
B. Adhikary, “A new type of higher associate cyclical association schemes,” Calcutta Statistical Association Bulletin, vol. 16, no. 1, pp. 40–44, Mar. 1967.
