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Nonparametric Density Estimation from Censored Data

Meghan S. O'Malley


This paper explores the accuracy of a simple density estimator, based solely on one histogram, for a variety of possible distribution shapes and bin/sample size combinations, through a simulation study. The density estimator is a piecewise quadratic polynomial chosen to match histogram areas with boundary points initially at midpoints of adjacent histogram bars then improved for smoothness. Performance is measured by the Mean Integrated Squared Error of the density estimates themselves and the Mean Square Errors of the means and a few percentiles derived from the density estimates. To give insight into the performance of this density estimator in practice, the piecewise quadratic density estimator is applied to wage data from the Bureau of Labor Statistics and compared to kernel density estimates using corresponding point data.