Exploring the Robustness of Ratio Estimators under Normal and Non-Normal Response: A Monte Carlo Markov-Chain Approach

An estimator is considered effective when it meets key inferential properties, such as unbiasedness, efficiency, consistency, and sufficiency. This research presents a simulation study on different ratio estimators using likelihood-based Markov-Chain Monte Carlo (MCMC) or nested sampling with both normal and non-normal response variables. Ratio estimators are essential in statistical inference, valued for their unbiasedness, efficiency, consistency, and sufficiency. However, their performance can be compromised when the underlying distributional assumptions are violated. Despite their theoretical advantages, ratio estimators' effectiveness can be significantly impacted when the underlying distributional assumptions such as normality are violated. This issue is particularly relevant in real-world applications where data often deviate from the ideal normal distribution, displaying characteristics like skewness, heavy tails, or outliers. This research aims to address this issue by evaluating various ratio estimators through a comprehensive simulation study. The study compares the performance of these estimators under both normal and non-normal conditions, using key metrics such as bias, mean squared error (MSE), and variance of ranks to determine how well these estimators maintain their desirable properties in the face of non-normality. By systematically evaluating these metrics, the research provides valuable insights into which ratio estimators are most reliable when the normality assumption is not met, offering practical guidance for statisticians and researchers working with real-world data that frequently deviates from idealized conditions.