The efficient estimation of population mean with level-and-rank auxiliary information under non-response: Cases studies in innovation chain and radiation sectors

Non-response is a serious problem in survey sampling, as it can increase estimation error and bias finite population inference. The purpose of this study is to design an efficient class of estimators for the finite population mean that combines level and rank auxiliary information across different non-response scenarios. The proposed estimator is a methodologically combined estimator that combines ratio adjustment, regression correction, exponential transformation, and the rank of the auxiliary variable in a simple random sampling without replacement (SRSWOR) context. Two types of non-response are considered: non-response in the study variable and multiple non-response of the study and auxiliary variables. The bias and mean-squared error (MSE) are calculated using first-order Taylor series approximations, and analytical efficiency conditions are defined. Then, the methodology is evaluated with numerical examples and using actual data from various fields in radiation science and AI compute/data infrastructure, as well as with a Monte Carlo simulation study with varying sample size, non-response percentages, subsampling factors, correlation levels, and non-response mechanisms. The numerical results demonstrate that the proposed estimator achieves significant improvements in MSE and PRE compared to various conventional estimators, with an efficiency gain of more than 81% over the classical ratio estimator (CR) for Population-I. The simulation results also show a wide range of non-response scenarios without compromising stability and competitiveness. The results suggest that integrating auxiliary level and rank information is a flexible and efficient method for estimating finite populations in surveys with nonresponse, as well as in other applications such as public health, environmental monitoring, and technological forecasting.