MATLAB Code Implementation for Kernel Density Estimation

A commonly used method for kernel density estimation is bandwidth selection. This approach effectively estimates two-dimensional scale parameters, though methods for higher-dimensional data continue to be developed. For high-dimensional scenarios, a recommended practice involves conducting multiple experiments to identify optimal values through iterative testing. Additionally, dimensionality reduction techniques like Principal Component Analysis (PCA) can be employed to map high-dimensional data into lower-dimensional spaces for more efficient estimation. In MATLAB implementation, key functions like ksdensity (for univariate KDE) can be extended for 2D cases using meshgrid and vectorized operations. For bandwidth optimization, functions like fminsearch can minimize the mean integrated squared error (MISE) through cross-validation. Various kernel functions are available for density estimation and probability density function fitting, including the Gaussian kernel (smooth estimation with infinite support) and Epanechnikov kernel (efficient finite-support estimator). The typical implementation involves: 1. Data normalization using zscore or similar functions 2. Bandwidth matrix calculation via Silverman's rule or plugin estimators 3. Kernel function evaluation using vectorized distance calculations 4. Density surface generation through 2D convolution or direct summation Code structure often includes parameter tuning loops for optimal bandwidth selection, with visualization using surf or contour plots for result validation.