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Theoretical properties of bandwidth selectors for kernel density estimation on the circle

Author

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  • Yasuhito Tsuruta

    (Wakayama Prefectural Office)

  • Masahiko Sagae

    (Kanazawa University)

Abstract

We derive the asymptotic properties of the least squares cross-validation (LSCV) selector and the direct plug-in rule (DPI) selector in the kernel density estimation for circular data. The DPI selector has a convergence rate of $$O(n^{-5/14})$$O(n-5/14), although the rate of the LSCV selector is $$O(n^{-1/10})$$O(n-1/10). Our simulation shows that the DPI selector has more stability than the LSCV selector for small and large sample sizes. In other words, the DPI selector outperforms the LSCV selector in theoretical and practical performance.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:72:y:2020:i:2:d:10.1007_s10463-018-0701-x
    DOI: 10.1007/s10463-018-0701-x
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    References listed on IDEAS

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    1. K. V. Mardia, 1999. "Directional statistics and shape analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 949-957.
    2. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
    3. Marco Marzio & Stefania Fensore & Agnese Panzera & Charles C. Taylor, 2018. "Circular local likelihood," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(4), pages 921-945, December.
    4. Toshihiro Abe & Arthur Pewsey, 2011. "Sine-skewed circular distributions," Statistical Papers, Springer, vol. 52(3), pages 683-707, August.
    5. Tsuruta, Yasuhito & Sagae, Masahiko, 2017. "Higher order kernel density estimation on the circle," Statistics & Probability Letters, Elsevier, vol. 131(C), pages 46-50.
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    Cited by:

    1. 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.
    2. Jan Beran & Britta Steffens & Sucharita Ghosh, 2022. "On nonparametric regression for bivariate circular long-memory time series," Statistical Papers, Springer, vol. 63(1), pages 29-52, February.

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