On bin–based density estimation

Abstract

We contribute to the study of data binning in density estimation.The particular disadvantage of histograms due to the effect of bin edge placement is stressed (again).We investigate how simple methods, both existing (such as the frequency polygon) and novel (proposing other natural piecewise linear adaptations), improve on the basic histogram (and on each other).Lurking in the background throughout are links with kernel density estimation.

Keywords:

• Bin edges
• Frequency polygon
• Kernel density estimation
• Histogram
• Linear binning
• Piecewise linearity
• Shifted histogram