ABSTRACT
Kernel Density Estimation (KDE) is a statistical technique that estimates the Probability Density Function (PDF). In this study, we investigate the impact of different kernel functions on the accuracy and characteristics of KDE. The kernel functions considered include Uniform, Epanechnikov, Gaussian, Triangular, and Biweight kernels. Each kernel function contributes weight to the overall density estimate based on proximity, significantly affecting the smoothness and characteristics of the density estimate.
We investigate the mathematical properties of each kernel function, such as their smoothness, bias, and variance, and how these properties affect the estimation process. We evaluate the efficiency of each kernel function by comparing it with the Epanechnikov kernel, which is known for its efficiency and serves as a benchmark in KDE. The efficiency of each kernel function was determined by a formula that considers the Epanechnikov Kernel's normalization constant and the evaluated kernel.
Our study provides a comparative analysis of kernel functions focusing on their efficiency relative to the Epanechnikov kernel. We found that the Epanechnikov kernel performed the best, demonstrating optimal performance by minimizing Mean Integrated Square Error (MISE). The Biweight kernel also showed robustness, especially in handling outliers effectively. It is crucial to choose the appropriate kernel function based on the specific characteristics of the dataset under consideration. Factors such as distribution complexity and the presence of outliers play a significant role in determining the most suitable kernel function.
