Efficient Estimator of a Finite Population Mean Using Two Auxiliary Variables and Numerical Application in Agricultural, Biomedical, and Power Engineering

Abstract

To improve the efficiency of an estimator with two auxiliary variables, we propose a new estimator of a finite population mean under simple random sampling. The bias and mean square error expressions of the proposed estimator have been obtained. In a comparison study, we found that the new estimator was consistently better than those of Abu-Dayyeh et al., Kadilar and Cingi, and Malik and Singh, as well as the regression estimator using two auxiliary variables, and that the minimum MSE values of the previous three above reported estimators were equal. We used four numerical examples in agricultural, biomedical, and power engineering to support these theoretical results, thus enriching the theory of survey samples by the development of new estimators with two auxiliary variables.

Visualization of generalized mean estimators using auxiliary information in survey sampling

“…For combining a regression estimator with a generic function in the ratio part, see for instance (Lu, 2017;Shabbir, Gupta, and Ahmed, 2018) for the first alternative model and (Kadilar and Cingi, 2005) for the second alternative model. With generic functions introduced in the ratio part, this underlines the generality of the parametric estimators through the function f θ (.…”

“…In comparaison to the Rao estimator (Rao, 1991;Lu, 2017), the combined estimatord adds new terms in the general expression (11), hence may be able to improve the mse for some populations. As an example, the estimatorȳ R c f andȳ R c4 f are considered nextafter in the generalized cases while the other combined estimators (regression and additive) are left for perspective.…”

Hartley-Ross Type Unbiased Estimators of Population Mean Using Two Auxiliary Variables

“…Using a general linear transformation of auxiliary information in the Shabbir and Gupta [11] estimator, we get: ( y SG;Gen ) = q 9 y + q 10 X x + q 11 Z z exp " X x X + x + 2 # :…”

“…In the process of conducting sample surveys, researchers normally use ratio-type estimators when there is a need to estimate the unknown population parameters of the study variable by means of known population parameters of a correlated auxiliary variable(s). An eye view of literature on the estimation of population mean under simple random sampling without replacement (SRSWOR) with proper information on two auxiliary variables shows prominent studies of Abu-Dayyeh et al [1], Kadilar and Cingi [2], Singh and Tailor [3], Lu and Yan [4], Lu et al [5], Vishwakarma and Kumar [6], Sharma and Singh [7], Yasmeen et al [8], Lu [9], Muneer et al [10], and Shabbir and Gupta [11].…”

Robust Estimation of Finite Population Totals Using a Model Based Approach in the Presence of Two Auxiliary Variables

“…The use of auxiliary information in double sampling found out that the proposed estimators did perform better than the mean per unit estimator and also compared to the other estimators that don't utilize the auxiliary information and they are not asymptotically optimum with two auxiliary variables [10].…”