The choice of bandwidth (smoothing parameter) is one of the central problems of density estimation. As we noted in previous inserts (Salgado-Ugarte et al. 1993, 1995), there are several ways to select an appropriate value for this parameter for histograms, frequency polygons (FPs), averaged shifted histograms (ASH/WARP estimators) and kernel estimators. Some of these selection methods focus on the optimal number of intervals, while others approximate the optimal bin width by minimizing an error measurement under specified conditions. In this insert, we survey a variety of methods for selecting the bandwidth for univariate density estimation. We also present several programs that determine useful reference values for the bandwidth when analyzing densities by means of histograms, FPs, and kernel density estimators, including the average shifted histogram (ASH) and the more general weighted averages of rounded poins (WARP). In addition, we include a new, integrated version of our previous programs for univariate density estimation.
