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2024 | 25 | nr 3 | 1--12
Tytuł artykułu

A Comprehensive Exploration of Complete Cross-Validation for Circular Data

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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)
Słowa kluczowe
Rocznik
Tom
25
Numer
Strony
1--12
Opis fizyczny
Twórcy
  • University of Defence, Brno, Czech Republic
  • Masaryk University, Brno, Czech Republic
autor
  • University of Defence, Brno, Czech Republic
  • Masaryk University, Brno, Czech Republic
Bibliografia
  • 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.
  • Bowman, A. W., (1984). An alternative method of cross-validation for the smoothing of density estimates. Biometrika, 71, pp. 353-360.
  • 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.
  • Hall, P., Marron, J. S., (1987). Estimation of integrated squared density derivatives. Statistics and Probability Letters, 6, pp. 109-115.
  • Hall, P., Watson, G. S., Cabrera, J., (1987). Kernel density estimation with spherical data. Biometrika, 74, pp. 751-762.
  • 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.
  • Jammalamadaka, S. R., SenGupta, A., (2001). Topics in circular statistics, Singapore: World Scientific.
  • Jones, M., Kappenman, R., (1991). On a class of kernel density estimate bandwidth selectors. Scandinavian Journal of Statistics, 19, pp. 337-349.
  • Ley, C., Verdebout, C., (2017). Modern directional statistics, Boca Raton: CRC Press.
  • Mardia, K. V., Jupp, P. E., (2000). Directional statistics, Chichester: Wiley.
  • 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.
  • 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.
  • Rudemo, M., (1982). Empirical choice of histograms and kernel density estimators. Scandinavian Journal of Statistics, 9, pp. 65-78.
  • Scott, D. W., (1992). Multivariate density estimation: Theory, practice, and visualization, New York: Wiley.
  • Silverman, B. W., (1986). Density estimation for statistics and data analysis, London: Chapman and Hall.
  • Taylor, C. C., (2008). Automatic bandwidth selection for circular density estimation. Computational Statistics and Data Analysis, 52, pp. 3493-3500.
  • Tsuruta, Y., Sagae, M., (2017). Higher order kernel density estimation on the circle. Statistics and Probability Letters, 131, pp. 46-50.
  • 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.
  • Wand, M. P., Jones, M. C., (1995). Kernel smoothing, London: Chapman and Hall.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171696627

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