The Epanechnikov kernel is a type of probability density function used in non-parametric statistics for kernel density estimation. It is defined as a quadratic function that is zero outside a certain range, making it efficient for estimating the distribution of data points. The kernel is particularly favored for its optimal properties in minimizing mean integrated squared error. This kernel is named after the Russian mathematician V. A. Epanechnikov, who introduced it in the 1960s. Its shape resembles a parabola, which allows it to provide a smooth estimate of the underlying data distribution while reducing the influence of outliers. The Epanechnikov kernel is often compared to other kernels, such as the Gaussian kernel, for its performance in various statistical applications.