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The Stata Journal
Volume 14 Number 2: pp. 237-258

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Self-consistent density estimation

Joerg Luedicke
Yale University and University of Florida
Gainesville, FL
Alberto Bernacchia
Jacobs University Bremen
Bremen, Germany
Abstract.  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.
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View all articles by these authors: Joerg Luedicke, Alberto Bernacchia

View all articles with these keywords: scdensity, density estimation, kernel density, nonparametric statistics, self-consistent density estimator

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