Paper #133

Títol:

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

Autors:

Jeffrey S. Simonoff i Frederic Udina

Data:

Juliol 1995

Resum:

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.

Paraules clau:

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

Codis JEL:

C10, C13, C43

Àrea de Recerca:

Estadística, Econometria i Mètodes Quantitatius

Publicat a:

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

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