A generalized estimation scheme under simple random sampling: Structural principles and interpretations for sports training and radiation data

Estimating the finite population mean is one of the main aims of survey sampling. It is well known that using auxiliary information can greatly improve the efficiency of estimators based on simple random sampling (SRS). Nonetheless, conventional estimators tend not to exploit available auxiliary information fully, thereby limiting their practical performance. To overcome this limitation, this paper proposes a new class of estimators that efficiently combine the sample mean with other auxiliary information to achieve better estimation accuracy without incurring the extra cost of collecting data. The theoretical characteristics of the proposed estimators, such as bias and mean squared error (MSE), are determined using first-order approximations, and the conditions under which they are better than existing estimators are identified. The three real datasets (sports and radiation studies) are used to evaluate the performance of the proposed estimators. The empirical results show substantial efficiency gains. In Population I, the proposed estimator has a Percentage Relative Efficiency (PRE) of around 238%, compared with 212% for the best existing estimator, representing an improvement of around 12%. In Population II, the proposed estimator has an amazingly high tolerance to negative correlation, achieving PRE values up to 359.6, almost twice the efficiency of traditional regression-type estimators (187%). When using the proposed estimator in Population III, the current estimators are already performing well, and the proposed estimator further reduces the MSE from 0.000400 to 0.000376 and increases PRE, which is already approximately 666 per cent. These findings support the validity of the proposed type of estimators, which have been found to significantly surpass traditional methods for estimating the population mean across various correlation structures and population characteristics, offering a robust, efficient, and practical framework for finite-population mean estimation in diverse applied settings.