Nonparametric Density Estimation - A Numerical Exploration

The simulation of distributions without parametric assumptions requires direct estimation of the underlying density function from sample data. Extensive literature discusses the theoretical aspects of this problem. This paper discusses application and practical implications of nonparametric density estimation. Primarily using piece-wise linear interpolation and the Nadaraya-Watson kernel regression methods, tests and experiments show the suitability of nonparametric methods for various circumstances. Nonparametric density estimation has the potential to support complex distributions, which would enable accurate simulation in a fully-automated environment.