Unbiased Estimator of Finite Population Variance Based on a Ratio Type Estimator


In this paper, an estimator of the finite population variance S2_y is proposed. The proposed estimator is exactly unbiased estimatorfor S2_y; further, the mean squared error (MSE) of the proposedestimator is derived. Empirical studies from real data sets are usedto compare the proposed estimator and other estimators proposed inthe literature. The proposed estimator is stable among otherfamilies and practically has minimum MSE among other estimators.

DOI Code: 10.1285/i20705948v11n1p196

Keywords: Hartely and Ross Estimator; Ratio Type Estimators; Finite Population Variance; Auxiliary Variable; Mean Squared Error; Simple Random Sample


Al-Jararha, J. (2008). Unbiased Ratio Estimation For Finite Populations. Ph. D. thesis, Colorado State University, Fort Collins, Co.

Cochran, W. G. (1977). Sampling Techniques (3rd ed.). New York: John Wiley & Sons.

Das, A. and T. Tripathi (1978). Use of auxiliary information in estimating the finite population variance. Sankhya C 40, 139-148.

Gupta, R. (1983). Unbiased estimation of nite population variance using auxiliary information. Statistics and Probability Letters 1(3), 121-124.

Hartley, H. O. and A. Ross (1954). Unbiased ratio estimates. Nature 174, 270-271.

Isaki, C. (1983). Variance estimation using auxiliary information. J Am Stat Assoc 78, 117-123.

Kadilar, C. and H. Cingi (2006). Ratio estimators for the population variance in simple and stratied random sampling. Appl Math Comput 35(1), 111-115.

Kadilar, C. and H. Cingi (2007). Improvement in variance estimation in simple random sampling. Communication of Statistics Theory and Methods 36(11), 2075-2081.

M. Rueda Garcia and A. Arcos Cebrian (1996). Repeated substitution method: The ratio estimator for population variance. Metrika 43, 101-105.

Prasad, B. and H. P. Singh (1992). Unbiased estimators of finite population variance using auxiliary information in sample surveys. Communications in Statistics-Theory

and Methods 21(5), 1367-1376.

Rao, T. J. and A. K. P. C. Swain (2014). A note on the hartley-ross unbiased ratio estimator. Communications in Statistics-Theory and Methods 43, 3162-3169.

Singh, H., L. Upadhyaya, and U. Namjoshi (1988). Estimation of nite population variance. Current Science 57, 1331-1334.

Singh, H. P. and R. S. Solanki (2013). A new procedure for variance estimation in simple random sampling using auxiliary information. Stat Papers 54, 479-497.

Upadhyaya, L. and H. Singh (1996). An estimator of population variance that utilizes the kurtosis of an auxiliary variable in sample surveys. Vikram Math J 19, 14-17.

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