Abstract
This paper develops a new approach to domain estimation and proposes a new class of ratio estimators that is more efficient than the regression estimator and not depending on any optimality condition using the principle of calibration weightings. Some well-known regression and ratio-type estimators are obtained and shown to be special members of the new class of estimators. Results of analytical study showed that the new class of estimators is superior in both efficiency and biasedness to all related existing estimators under review. The relative performances of the new class of estimators with a corresponding global estimator were evaluated through a simulation study. Analysis and evaluation are presented.
Similar content being viewed by others
References
Arnab, R., Singh, S.: A note on variance estimation for the generalized regression predictor. Aust. N. Z. J. Stat. 47(2), 231–234 (2005)
Clement, E.P.: Calibration approach separate ratio estimator for population mean in stratified sampling. Int. J. Mod. Math. Sci. 13(4), 377–384 (2015)
Clement, E.P.: An improved ratio estimator for population mean in stratified random sampling. Eur. J. Stat. Probab. 4(4), 12–17 (2016)
Clement, E.P.: Efficient exponential estimators of population mean in survey sampling. Int. J. Math. Comput. 28(3), 94–106 (2017)
Clement, E.P., Udofia, G.A., Enang, E.I.: Estimation for domains in stratified random sampling in the presence of non-response. Am. J. Math. Stat. 4(2), 65–71 (2014)
Clement, E.P., Enang, E.I.: Calibration approach alternative ratio estimator for population mean in stratified sampling. Int. J. Stat. Econ. 16(1), 83–93 (2015)
Clement, E.P., Enang, E.I.: On the efficiency of ratio estimator over the regression estimator. Commun. Stat. Theory Methods 46(11), 5357–5367 (2017)
Cochran, W.G.: Sampling techniques. Wiley, New York (1977)
Deville, J.C., Sarndal, C.E.: Calibration estimators in survey sampling. J. Am. Stat. Assoc. 87, 376–382 (1992)
Hansen, M.H., Hurwitz, W.N., Gurney, M.: The problems and methods of the Sample survey of business. J. Am. Stat. Assoc. 41, 173–189 (1946)
Hansen, M.H., Hurwitz, W.N., Madow, W.G.: Sample survey methods and theory. Wiley, New York (1953)
Kim, J.M., Sungur, E.A., Heo, T.Y.: Calibration approach estimators in stratified sampling. Stat. Probab. Lett. 77(1), 99–103 (2007)
Kim, J.K., Park, M.: Calibration estimation in survey sampling. Int. Stat. Rev. 78(1), 21–29 (2010)
Kott, P.S.: Using calibration weighting to adjust for non-response and coverage errors Survey. Methodology 32, 133–142 (2006)
Molefe, W.B.: Sample design for small area estimation. University of Wollongong. Research online. 18 July 2012. http://ro.uow.edu.au/theses/3495 (2011)
Onyeka, A.C.: Estimation of population mean in post-stratified sampling using known value of some population parameter(s). Stat. Transit. New Series 13(1), 65–78 (2012)
Rao, D., Khan, M.G.M., Khan, S.: Mathematical programming on multivariate calibration estimation in stratified sampling. World Acad. Sci. Eng. Technol. 72, 12–27 (2012)
Sarndal, C.-E.: The calibration approach in survey theory and practice. Surv. Methodol. 33, 99–119 (2007)
Sharma, B., Tailor, R.: A new ratio-cum-dual to ratio estimator of finite population mean in simple random sampling. Glob. J. Sci. 10(1), 27–31 (2010)
Singh, H.P., Kakran, M.S.: A modified ratio estimator using known coefficient of kurtosis of an auxiliary character. J. Indian Soc. Agric. Stat. 45(2), 65–71 (1993)
Singh, H.P., Tailor, R.: Use of known correlation coefficient in estimating the finite population mean. Stat. Transit. 6(4), 555–560 (2003)
Singh, H.P., Vishwakarma, G.K.: Modified exponential ratio and product estimators for finite population mean in double sampling. Austrian J. Stat. 36(3), 217–225 (2007)
Singh, R., Audu, A.: Efficiency of ratio estimator in stratified random sampling using information on auxiliary attribute. Int. J. Eng. Innov. Technol. 2(1), 116–172 (2013)
Upadhyaya, L.N., Singh, H.P.: Use of transformed auxiliary variable in estimating the finite population mean. Biom. J. 41(5), 627–636 (1999)
Vishwakarma, G.K., Singh, H.P.: Separate ratio-product estimator for estimating population mean using auxiliary information. J. Stat. Theory Appl. 10(4), 653–664 (2011)
Yan, Z., Tian, B.: Ratio method to the mean estimation using coefficient of skewness of auxiliary variable. In: ICICA, Part III, CCIC, vol. 106, pp. 103–110 (2010)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Enang, E.I., Clement, E.P. An Efficient Class of Calibration Ratio Estimators of Domain Mean in Survey Sampling. Commun. Math. Stat. 8, 279–293 (2020). https://doi.org/10.1007/s40304-018-00174-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40304-018-00174-z
Keywords
- Auxiliary variable
- Calibration approach
- Efficiency
- Global estimator
- Ratio-type estimator
- Stratified sampling
- Study variable