Kernel bandwidth estimation for non-parametric density estimation: a comparative study

We investigate the performance of conventional bandwidth estimators for non-parametric kernel density estimation on a number of representative pattern-recognition tasks, to gain a better understanding of the behaviour of these estimators in high-dimensional spaces. We show that there are several regularities in the relative performance of conventional kernel bandwidth estimators across different tasks and dimensionalities. In particular, we find that the Silverman ruleof-thumb and maximal-smoothing principle estimators consistently perform competitively on most tasks and dimensions for the datasets considered. Keywords—non-parametric density estimation; kernel density estimation; kernel bandwidth estimation, pattern recognition I. KERNEL DENSITY ESTIMATION Kernel Density Estimators (KDEs) estimate the nonparametric density function of a set of D-dimensional iid data samples, X, as the sum of parametric functions, where the parametric function is known as a kernel and is centred on each sample. More formally, the density of a data point x, can be estimated as