Abstract: Given a set of observations, the knowledge of the underlying probability density function that generates the sample is often of interest. Kernel Density Estimation is a nonparametric method used to guess the underlying density function using the sample observations. Although arguably the most popular method of density estimation, KDE is not free from drawbacks. This method of estimation varies greatly with the choice of the smoothing parameter used to estimate the density. This paper gives an overview of the KDE and discusses some statistical properties of the ideal estimator used to guess the unknown density.An outline of some existing methods of choosing a smoothing parameter are discussed. Here we only consider estimation under the univariate setup. The idea of KDE can easily be generalized to a multivariate dataset.
Keywords: Kernel density estimation, bandwidth, smoothing parameter, kernel, least squares cross validation, mean integrated square error