Log-Ratio Estimation in Survey Sampling: A Comparative Study Using Agricultural and Cancer Data with Simulations

Abstract

The estimation of finite population characteristics, particularly the mean, is critical in survey sampling, as it has a direct impact on the validity of sample data results. As the number and complexity of available data increases, so does the demand for more robust and precise estimators. Traditional estimators frequently fail to take full advantage of auxiliary information, which can be critical for enhancing estimating accuracy. This paper presents a novel log-ratio estimator that incorporates auxiliary information in a non-linear manner using logarithmic transformations of the study and auxiliary variables. The log-ratio estimator's performance is assessed against 9 different classical and modern estimators using two essential metrics: mean squared error (MSE) and percentage relative efficiency. Our empirical analysis includes a variety of applications, such as estimating the area under wheat based on cultivated area, estimating peppermint oil production based on field area, and three real-world datasets: breast cancer deaths, cancer deaths by gender (male and female), and brain tumor survival rates. To supplement these applications, a simulation study with a population size of 100,000 and a sample size of 1,000 was run up to 100,000 times to assess the estimators’ resilience and stability. The empirical and simulation results consistently reveal that the log-ratio estimator produces lower MSE and higher PRE values across all datasets, exhibiting greater accuracy and efficiency over traditional estimators. These findings suggest that the log-ratio estimator gives more trustworthy and efficient estimates, particularly when dealing with complicated data. As such, this estimator is a promising tool for future survey sampling, helping to enhance estimating methodologies capable of dealing with the challenges provided by modern, large-scale datasets.