Mean Estimation under Median Ranked Set Sampling with an Application to Farm Credit Data

Accepted March 2026

Abstract

Median Ranked Set Sampling (MRSS) is a sampling method that helps estimate the population mean more accurately by using ranking information, especially when an auxiliary variable related to the main variable is easy to rank. This approach is often used in fields
like agriculture and economics, where it is cheaper and simpler to collect auxiliary data than to measure the main variable directly. In this study, we introduce a new exponential logarithmic estimator for the population mean within the MRSS framework. This estimator uses auxiliary information to improve efficiency and reduce mean squared error, making it useful for cases with strongly related variables, such as farm credit and financial data. We show how this method works using a real farm credit dataset, where real estate farm loans are the main variable and non-real-estate farm state loans are the auxiliary variable. This example shows how MRSS-based estimation can help with financial planning, agricultural policy, and resource allocation. We also run a detailed simulation study with different correlation levels and sample setups to test the estimator’s performance. The results show that our estimator is robust and more efficient than existing methods in many realistic situations.