A Family of Unbiased Modified Linear Regression Estimators

J. Subramani

doi:10.15415/mjis.2015.41008

Authors

J. Subramani Department of Statistics, Pondicherry University, Puducherry-605014, India

DOI:

https://doi.org/10.15415/mjis.2015.41008

Keywords:

Auxiliary variable, Efficiency, Mean squared error, Population Mean, Simple random sampling

Abstract

In this paper, a family of modified linear regression estimators has been proposed which are unbiased. The variance of the proposed estimators and the conditions for which the proposed estimators perform better than the classical ratio estimator and the existing modified ratio estimators have been obtained. Further, we have shown that the classical ratio estimator, the existing modified ratio estimators, and the usual linear regression estimator are the particular cases of the proposed estimators. It is observed from the numerical study that the proposed estimators perform better than the ratio estimator and the existing modified ratio estimators.

Downloads

Download data is not yet available.

References

Cochran, W.G. (1977).Sampling techniques, Third Edition, USA, Wiley Eastern Limited

Kadilar, C. and Cingi, H. Ratio estimators in simple random sampling. Applied Mathematics and Computation, 151, 893-902, (2004). http://dx.doi.org/10.1016/S0096-3003(03)00803-8

Kadilar, C. and Cingi, H. An Improvement in estimating the population means by using the Correlation Coefficient. Hacettepe Journal of Mathematics and Statistics, 35(1), 103-109, (2006).

Murthy, M.N. (1967). Sampling theory and methods. Calcutta, India, Statistical Publishing Society

Singh, D. and Chaudhary, F.S. (1986). Theory and analysis of sample survey designs. New Delhi, New Age International Publisher

Singh, H.P. and Tailor, R. Use of known correlation coefficient in estimating the finite population means. Statistics in Transition, 6 (4), 555-560, (2003).

Singh, H.P., Tailor, R., Tailor, R., and Kakran, M.S. An improved estimator of a population mean using power transformation, Journal of the Indian Society of Agricultural Statistics, 58(2), 223-230, (2004).

Sisodia, B.V.S. and Dwivedi, V.K. (1981). A modified ratio estimator using coefficient of variation of auxiliary variable. Journal of the Indian Society of Agricultural Statistics, 33(1), 13-18, (1981).

Subramani, J. and Kumarapandiyan, G. A class of modified linear regression estimators for estimation of finite population mean, Journal of Reliability and Statistical Studies, 5(2),1-10, (2012).

Upadhyaya, L.N and Singh, H.P. Use of a transformed auxiliary variable in estimating the finite population means. Biometrical Journal, 41 (5), pp 627-636, (1999). http://dx.doi.org/10.1002/(SICI)1521-4036(199909)41:5%3C627::AID-BIMJ627%3E3.0.CO;2-W

Yan, Z. and Tian, B. (2010). Ratio method to the mean estimation using the coefficient of skewness of auxiliary variable, ICICA 2010, Part II, CCIS, 106, pp. 103–110. http://dx.doi.org/10.1007/978-3-642-16339-5_14