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Automatic data-based bin width selection for rose diagram

Author

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  • Yasuhito Tsuruta

    (The University of Nagano)

  • Masahiko Sagae

    (Kanazawa University)

Abstract

A rose diagram is a representation that circularly organizes data with the bin width as the central angle. This diagram is widely used to display and summarize circular data. Some studies have proposed the selector of bin width based on data. However, only a few papers have discussed the property of these selectors from a statistical perspective. Thus, this study aims to provide a data-based bin width selector for rose diagrams using a statistical approach. We consider that the radius of the rose diagram is a nonparametric estimator of the square root of two times the circular density. We derive the mean integrated square error of the rose diagram and its optimal bin width and propose two new selectors: normal reference rule and biased cross-validation. We show that biased cross-validation converges to its optimizer. Additionally, we propose a polygon rose diagram to enhance the rose diagram.

Suggested Citation

  • Yasuhito Tsuruta & Masahiko Sagae, 2023. "Automatic data-based bin width selection for rose diagram," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(5), pages 855-886, October.
    • Handle: RePEc:spr:aistmt:v:75:y:2023:i:5:d:10.1007_s10463-023-00868-4
    DOI: 10.1007/s10463-023-00868-4
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    References listed on IDEAS

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    1. Tsuruta, Yasuhito & Sagae, Masahiko, 2017. "Higher order kernel density estimation on the circle," Statistics & Probability Letters, Elsevier, vol. 131(C), pages 46-50.
    2. Taylor, Charles C., 2008. "Automatic bandwidth selection for circular density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3493-3500, March.
    3. Kanazawa, Yuichiro, 1993. "Hellinger distance and Akaike's information criterion for the histogram," Statistics & Probability Letters, Elsevier, vol. 17(4), pages 293-298, July.
    4. Toshihiro Abe & Arthur Pewsey, 2011. "Sine-skewed circular distributions," Statistical Papers, Springer, vol. 52(3), pages 683-707, August.
    5. Yasuhito Tsuruta & Masahiko Sagae, 2020. "Theoretical properties of bandwidth selectors for kernel density estimation on the circle," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 511-530, April.
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