scdensity: A program for self-consistent density estimation

Estimating the density of a distribution from a finite number of data points is an important tool in the statistician's and data analyst's toolbox. In their recent paper, Bernacchia and Pigolotti (JRSS-B, 2011) introduce a new non-parametric method for the density estimation of univariate distributions. Whereas conventional methods, like plotting histograms or kernel density estimates, rely on the need to make arbitrary choices beforehand (e.g., choosing a smoothing parameter), Bernacchia and Pigolotti's approach does not rely on any a priori assumptions but estimates the density in a `self-consistent' way by iteratively finding an optimal shape of the kernel. The method of self-consistent density estimation is implemented in Stata as an ado-file (-scdensity-), with its main engine written in Mata. The underlying theory and main features of this program will be discussed. In addition, results of Monte Carlo simulations will be presented comparing the performance of the self-consistent density estimate with various kernel estimates and Maximum Likelihood fits. Finally, the potential usefulness of the self-consistent estimator in other contexts such as non-parametric regression modeling will be evaluated.