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The essential histogram

Author

Listed:
  • Housen Li
  • Axel Munk
  • Hannes Sieling
  • Guenther Walther

Abstract

SummaryThe histogram is widely used as a simple, exploratory way of displaying data, but it is usually not clear how to choose the number and size of the bins. We construct a confidence set of distribution functions that optimally deal with the two main tasks of the histogram: estimating probabilities and detecting features such as increases and modes in the distribution. We define the essential histogram as the histogram in the confidence set with the fewest bins. Thus the essential histogram is the simplest visualization of the data that optimally achieves the main tasks of the histogram. The only assumption we make is that the data are independent and identically distributed. We provide a fast algorithm for computing the essential histogram and illustrate our method with examples.

Suggested Citation

  • Housen Li & Axel Munk & Hannes Sieling & Guenther Walther, 2020. "The essential histogram," Biometrika, Biometrika Trust, vol. 107(2), pages 347-364.
    • Handle: RePEc:oup:biomet:v:107:y:2020:i:2:p:347-364.
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    File URL: http://hdl.handle.net/10.1093/biomet/asz081
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    Cited by:

    1. Tisdall, Lucas & Zhang, Yahua & Zhang, Anming, 2021. "COVID-19 impacts on general aviation – Comparative experiences, governmental responses and policy imperatives," Transport Policy, Elsevier, vol. 110(C), pages 273-280.
    2. Zelaya Mendizábal, Valentina & Boullé, Marc & Rossi, Fabrice, 2023. "Fast and fully-automated histograms for large-scale data sets," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).

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