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

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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.

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  • Jeffrey S. Simonoff & Frederic Udina, 1995. "Measuring the stability of histogram appearance when the anchor position is changed," Economics Working Papers 133, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:133
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    1. HARDLE, Wolfgang & SCOTT, David, 1990. "Smoothing by weighted averaging of rounded points," LIDAM Discussion Papers CORE 1990040, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    1. repec:jss:jstsof:05:i03 is not listed on IDEAS
    2. Jyh-Shyang Wu & Wen-Shuenn Deng, 2012. "Averaged shifted chi-square test," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 39-57.
    3. Udina, Frederic, 2000. "Implementing interactive computing in an object-oriented environment," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 5(i03).
    4. Dong, Jianping & Zheng, Chuang, 2001. "Generalized edge frequency polygon for density estimation," Statistics & Probability Letters, Elsevier, vol. 55(2), pages 137-145, November.
    5. Pedro Delicado & Manuel del Río, 1999. "A generalization of histogram type estimators," Economics Working Papers 422, Department of Economics and Business, Universitat Pompeu Fabra.

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    More about this item

    Keywords

    Bin width; frequency polygon; Gini index; linear binning; Lorenz curve; Monte Carlo simulation;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation

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