A Regression Estimator in Path Sampling

It is known that regression estimation utilizes known auxiliary information to develop efficient estimators. The objective of this paper is to propose a regression estimator in path sampling to improve the precision of estimators of the population mean by using generalized regression estimation with unequal probability sampling when the relationship between the variable of interest and auxiliary variable is linear with a straight line that does not pass through the origin. The mean square error of this proposed regression estimator and the estimator of this mean square error are obtained. The efficiency of the proposed regression estimator is investigated by simulation study on the real world data, and the estimated mean square error of the proposed regression estimator is compared to two original existing estimators, which are an unbiased estimator and ratio estimator. The simulation results show that the proposed regression estimator has very small estimated bias, and it is more efficient than those two original estimators.