A performance comparison of KDE fixed-bandwidth selectors in density estimation

Kernel Density Estimation stands as the foundation for most contemporary non-parametric probability density function estimation methods. The essence of this technique centers around the bandwidth parameter, and a variety of bandwidth selectors have been created to precisely determine the optimal value for refinement. Despite the existence of numerous articles on this topic, selecting an appropriate method for a specific database remains a challenging issue, and it continues to be an active area of research. This work explores classic and prominent bandwidth selectors with the intention of evaluating their performance, specifically in terms of the error area between the model and its estimation, across different scenarios. Fourteen methods are evaluated in total, comprising six Plug-in and eight Cross-validation based methods. This research provides fresh perspectives on the subject by conducting a comparative study encompassing a diverse set of distributions varying in complexity and a wide range of sample sizes. In addition, it includes a comparison of KDE methods that have not been previously assessed together. This paper provides an in-depth exploration of the distinctions among the examined methods, providing means for a conscious choice of which bandwidth selector to use based on some prior knowledge of the experiment in hand and its data characteristics. Among the tested approaches, some methods show remarkable robustness and accuracy, particularly in handling complex distributions. Key challenges, such as overestimating or underestimating bandwidth, were identified and addressed, offering improved solutions for diverse scenarios.