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Multivariate Ratio Estimator of the Population Total under Stratified Random Sampling

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DOI: 10.4236/ojs.2012.23036    4,979 Downloads   8,663 Views   Citations


Olkin [1] proposed a ratio estimator considering p auxiliary variables under simple random sampling. As is expected, Simple Random Sampling comes with relatively low levels of precision especially with regard to the fact that its variance is greatest amongst all the sampling schemes. We extend this to stratified random sampling and we consider a case where the strata have varying weights. We have proposed a Multivariate Ratio Estimator for the population mean in the presence of two auxiliary variables under Stratified Random Sampling with L strata. Based on an empirical study with simulations in R statistical software, the proposed estimator was found to have a smaller bias as compared to Olkin’s estimator.

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The authors declare no conflicts of interest.

Cite this paper

O. Ngesa, G. Orwa, R. Otieno and H. Murray, "Multivariate Ratio Estimator of the Population Total under Stratified Random Sampling," Open Journal of Statistics, Vol. 2 No. 3, 2012, pp. 300-304. doi: 10.4236/ojs.2012.23036.


[1] I. Olkin, “Multivariate Ratio Estimation for Finite Populations,” Biometrika, Vol. 45, No. 1-2, 1956, pp. 154-165.
[2] W. G. Cochran, “Sampling Techniques,” 3rd Edition, Wiley, New York, 1977.
[3] L. Y. Deng and R. S. Chikura, “On the Ratio and Regression Estimation in Finite Population Sampling,” American Statistician, Vol. 44, No. 4, 1990, pp. 282-284.
[4] P. V. Sukhatme and B. V. Sukhatme, “Sampling Theories of Survey with Applications,” Iowa State University Press, Ames, 1970.

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