Improved estimation of population mean using dual auxiliary information under simple random sampling: Applications to accounting, machinery and radiation data

One of the fundamental problems in survey sampling is efficiently estimating the finite population mean, especially when auxiliary information is available. Auxiliary variables have long been known to be a useful tool for increasing the precision of an estimator based on simple random sampling (SRS). Most current estimators, however, use only one auxiliary variable or do not fully make use of the joint information provided by several correlated auxiliary variables which leads to suboptimal estimation efficiency. This study aims to present an improved estimator for the finite population mean based on simple random sampling without replacement, using dual auxiliary information. First-order approximation is used to obtain theoretical properties of the proposed estimator such as its bias and mean squared error (MSE). The superiority of the proposed estimator over other conventional estimators (such as sample mean, ratio estimator, regression estimator, product estimator, exponential estimators, and some newly proposed dual auxiliary estimators) is demonstrated by analytical comparisons under certain regularity conditions. The theoretical results are testing using five real-life datasets of measurements in accounting, machinery production, and environmental radiation. The empirical results clearly show significant efficiency improvements in terms of the mean squared error (MSE) and percent relative efficiency (PRE) over other estimators. These results indicate that the proposed estimator offers a simple, robust and practically applicable alternative to improve the estimation of population means when reliable dual auxiliary information is available.