ABSTRACT
This study comprehensively evaluates and compares various bandwidth selection methods for kernel density estimation (KDE), a non-parametric technique used to estimate probability density functions from data. The choice of bandwidth significantly impacts the accuracy and reliability of KDE by controlling the smoothness of the density estimates and balancing the bias-variance trade-off.
The research implements and analyzes four major bandwidth selection techniques: Silverman's rule-of-thumb, least squares cross-validation (LSCV), biased cross-validation (BCV), and the Sheather-Jones plug-in estimator. Extensive experiments across diverse simulated and real-world datasets assess their performance using multiple metrics, including mean integrated squared error, visual inspection, goodness-of-fit tests, and computational efficiency measures.
The findings reveal the relative strengths and limitations of each method. Silverman's rule-of-thumb stands out for its simplicity, consistent low error rates, and high computational efficiency across various sample sizes and distributions. The Sheather-Jones plug-in estimator also demonstrates competitive accuracy with faster convergence compared to cross-validation approaches. In contrast, LSCV and BCV exhibit higher variability and computational costs, especially for larger datasets, despite being more data-driven. The study identifies optimal scenarios for each technique and provides guidelines to select the most suitable bandwidth selector based on data characteristics, accuracy requirements, and computational constraints.
