NEW METHODS FOR PARAMETRIC AND NONPARAMETRIC HIGH ORDER KERNEL DENSITY ESTIMATION
The Kernel Density Estimation (KDE) method is seen here as the first step of the Expectation Maximization (EM) algorithm for estimating the density of a latent variable when the initial guess is the uniform distribution. The properties of the first EM step are then investigated for different choices of the starting density. When the KDE itself is chosen the asymptotic bias of the EM update has the opposite value of KDE while the variance order is maintained. Thus, the average of the EM update with the KDE reduces the best achievable mean integrated square error from n-4/5to n-8/9.