A Modified Population Mean Estimator for Sample Surveys with Nonresponse Problems

Challenges in data collection often emerge due to constraints such as limited time, labor, and budget, especially when dealing with large population sizes. These limitations make gathering information from every individual impractical, prompting researchers to adopt survey methodologies that focus on selecting representative samples. While this approach can streamline data collection, it introduces potential sources of error. Analyzing data from these samples can sometimes yield inaccurate statistical values, particularly when issues like incomplete sampling or non-responses in key variables arise. Such challenges can significantly impact the reliability of study findings. To tackle this issue, this paper introduces a new estimator for the population mean within the context of sample surveys, leveraging sub-sampling techniques. The proposed method is designed to handle scenarios where both study and auxiliary variables experience non-response, a common challenge in survey research. The paper also delves into the new estimator's mathematical properties, such as bias, mean squared error (MSE), and minimum MSE (MMSE), evaluating its efficiency using the percent absolute relative biases (PARBs) and the percent relative efficiencies (PREs) criterion. The study employs three real-world datasets to validate the proposed estimator's effectiveness. It also conducts theoretical analyses and empirical studies to compare the new estimator's performance against existing methods. The results consistently demonstrate that the new estimator provides superior accuracy and reliability, outperforming existing estimators under similar conditions. These findings highlight the potential of the proposed approach to improve data accuracy in survey research, especially in cases plagued by non-response issues.