Paper #133

Title:

Measuring the stability of histogram appearance when the anchor position is changed

Authors:

Jeffrey S. Simonoff and Frederic Udina

Date:

July 1995

Abstract:

Although the histogram is the most widely used density estimator, it is well--known that the appearance of a constructed histogram for a given bin width can change markedly for different choices of anchor position. In this paper we construct a stability index $G$ that assesses the potential changes in the appearance of histograms for a given data set and bin width as the anchor position changes. If a particular bin width choice leads to an unstable appearance, the arbitrary choice of any one anchor position is dangerous, and a different bin width should be considered. The index is based on the statistical roughness of the histogram estimate. We show via Monte Carlo simulation that densities with more structure are more likely to lead to histograms with unstable appearance. In addition, ignoring the precision to which the data values are provided when choosing the bin width leads to instability. We provide several real data examples to illustrate the properties of $G$. Applications to other binned density estimators are also discussed.

Keywords:

Bin width, frequency polygon, Gini index, linear binning, Lorenz curve, Monte Carlo simulation

JEL codes:

C10, C13, C43

Area of Research:

Statistics, Econometrics and Quantitative Methods

Published in:

Computational Statistics and Data Analysis, 23, (1997), pp. 335-353

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