Capturing Uncertainty in Gaussian Mixture-Based Entropy Estimation via Weighted Likelihood Bootstrap

Entropy estimation plays a crucial role in various fields, such as information theory, statistical data science, and machine learning. However, traditional entropy estimation methods often struggle with complex data distributions. Recently, mixture-based entropy estimation has been proposed and gained attention due to its ease of use and accuracy. This work proposes a novel approach based on the weighted likelihood bootstrap to quantify the uncertainty associated with mixture-based entropy estimation. Unlike standard methods, our approach leverages the underlying mixture structure by assigning random weights to observations in a weighted likelihood bootstrap procedure, leading to more accurate uncertainty estimation. The proposed approach is illustrated by analyzing the log-returns of Brent oil prices from NYMEX for the years 2014-2023. Quantifying the inherent randomness and its uncertainty offers valuable insights into the market's resilience, volatility patterns, and potential future trends. This study not only advances uncertainty estimation in mixture-based entropy but also provides a unique perspective on the dynamics of the oil market, with potential implications for risk management and investment strategies.