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Autor
Hasilová Kamila (University of Defence, Brno, Czech Republic), Horová Ivana (Masaryk University, Brno, Czech Republic), Vališ David (University of Defence, Brno, Czech Republic), Zámečník Stanislav (Masaryk University, Brno, Czech Republic)
Tytuł
A Comprehensive Exploration of Complete Cross-Validation for Circular Data
Źródło
Statistics in Transition, 2024, vol. 25, nr 3, s. 1-12, aneks, rys., bibliogr. 19 poz.
Słowa kluczowe
Estymacja, Analiza danych, Statystyka
Estimation, Data analysis, Statistics
Uwagi
summ.
Abstrakt
Kernel density estimation of circular data has recently received considerable attention for its ability to model and analyse distributions on unit circles and other periodic domains. Our aim is to contribute to the literature on data-driven bandwidth selectors in circular kernel density estimation. We propose a novel circular-specific method that is based on a crossvalidation procedure with a von Mises density used as a kernel function. Using simulated data as well as real-world circular datasets, we evaluate and validate the proposed method and compare it with the existing methods. (original abstract)
Dostępne w
Biblioteka Główna Uniwersytetu Ekonomicznego w Krakowie
Pełny tekst
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Bibliografia
Pokaż
  1. Baszczyńska, A., (2017). One value of smoothing parameter vs interval of smoothing parameter values in kernel density estimation. Acta Universitatis Lodziensis. Folia Oeconomica, 6, pp. 73-86.
  2. Bowman, A. W., (1984). An alternative method of cross-validation for the smoothing of density estimates. Biometrika, 71, pp. 353-360.
  3. García-Portugués, E., (2013). Exact risk improvement of bandwidth selectors for kernel density estimation with directional data. Electronic Journal of Statistics, 7, pp. 1655- 1685.
  4. Hall, P., Marron, J. S., (1987). Estimation of integrated squared density derivatives. Statistics and Probability Letters, 6, pp. 109-115.
  5. Hall, P., Watson, G. S., Cabrera, J., (1987). Kernel density estimation with spherical data. Biometrika, 74, pp. 751-762.
  6. Hisada, M., (1972). Azimuth orientation of the dragonfly (Sympetrum). In Galler, S. R., et al. Animal Orientation and Navigation, pp. 511-522. Washington: U.S. Government Printing Office.
  7. Jammalamadaka, S. R., SenGupta, A., (2001). Topics in circular statistics, Singapore: World Scientific.
  8. Jones, M., Kappenman, R., (1991). On a class of kernel density estimate bandwidth selectors. Scandinavian Journal of Statistics, 19, pp. 337-349.
  9. Ley, C., Verdebout, C., (2017). Modern directional statistics, Boca Raton: CRC Press.
  10. Mardia, K. V., Jupp, P. E., (2000). Directional statistics, Chichester: Wiley.
  11. Oliveira, M., Crujeiras, R. M., Rodríguez-Casal, A., (2012). A plug-in rule for bandwidth selection in circular density estimation. Computational Statistics and Data Analysis, 56, pp. 3898-3908.
  12. Oliveira, M., Crujeiras, R. M., Rodríguez-Casal, A., (2014). NPCirc: An R Package for Nonparametric Circular Methods. Journal of Statistical Software, 61, pp. 1-26.
  13. Rudemo, M., (1982). Empirical choice of histograms and kernel density estimators. Scandinavian Journal of Statistics, 9, pp. 65-78.
  14. Scott, D. W., (1992). Multivariate density estimation: Theory, practice, and visualization, New York: Wiley.
  15. Silverman, B. W., (1986). Density estimation for statistics and data analysis, London: Chapman and Hall.
  16. Taylor, C. C., (2008). Automatic bandwidth selection for circular density estimation. Computational Statistics and Data Analysis, 52, pp. 3493-3500.
  17. Tsuruta, Y., Sagae, M., (2017). Higher order kernel density estimation on the circle. Statistics and Probability Letters, 131, pp. 46-50.
  18. Tsuruta, Y., Sagae, M., (2020). Theoretical properties of bandwidth selectors for kernel density estimation on the circle. Annals of the Institute of Statistical Mathematics, 72, pp. 511-530.
  19. Wand, M. P., Jones, M. C., (1995). Kernel smoothing, London: Chapman and Hall.
Cytowane przez
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ISSN
1234-7655
Język
eng
URI / DOI
http://dx.doi.org/10.59170/stattrans-2024-024
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