Self-consistent density estimation

Estimating a continuous density function from a finite set of data points is an important tool in many scientific disciplines. Popular nonparametric density estimators include histograms and kernel density methods. These methods require the researcher to control the degree of smoothing inherent in an estimated function. In a recent approach, a new method for nonparametric density estimation was proposed that finds the estimate self-consistently, that is without requiring the researcher to choose a smoothing parameter a priori. In this article, we outline the basic ideas of the self-consistent density estimator, and we present a Stata implementation of the method. In addition, we present results of Monte Carlo simulations that show that the self-consistent estimator performs better than other methods, especially for larger data samples. Copyright 2014 by StataCorp LP.