Automatic bandwidth selection for circular density estimation. (English) Zbl 1452.62269

Summary: Given angular data \(\theta_{1},\dots ,\theta_n \in [0,2\pi)\) a common objective is to estimate the density. In case that a kernel estimator is used, bandwidth selection is crucial to the performance. A “plug-in rule” for the bandwidth, which is based on the concentration of a reference density, namely, the von Mises distribution is obtained. It is seen that this is equivalent to the usual Euclidean plug-in rule in the case where the concentration becomes large. In case that the concentration parameter is unknown, alternative methods are explored which are intended to be robust to departures from the reference density. Simulations indicate that “wrapped estimators” can perform well in this context. The methods are applied to a real bivariate dataset concerning protein structure.


62G07 Density estimation
62-08 Computational methods for problems pertaining to statistics


circular; CircStats; wle
Full Text: DOI Link


[1] Agostinelli, C., Robust estimation for circular data, Computational statistics and data analysis, 51, 5867-5875, (2007) · Zbl 1445.62054
[2] Fisher, N.I., Smoothing a sample of circular data, Journal of structural geology, 11, 775-778, (1989)
[3] Hall, P.; Watson, G.S.; Cabrera, J., Kernel density estimation with spherical data, Biometrika, 74, 751-762, (1987) · Zbl 0632.62033
[4] Jammalamadaka, S. Rao; SenGupta, A., Topics in circular statistics, (2001), World Scientific Singapore
[5] Jones, M.C.; Marron, J.S.; Sheather, S.J., A brief survey of bandwidth selection for density estimation, Journal of the American statistical association, 91, 401-407, (1996) · Zbl 0873.62040
[6] Klemelä, J., Estimation of densities and derivatives of densities with directional data, Journal of multivariate analysis, 73, 18-40, (2000) · Zbl 1054.62033
[7] Ko, D., Robust estimation of the concentration parameter of the von-Mises distribution, The annals of statistics, 20, 917-928, (1992) · Zbl 0746.62033
[8] Mardia, K.V.; Jupp, P.E., Directional statistics, (1999), John Wiley Chichester
[9] Marron, J.S.; Wand, M.P., Exact Mean integrated squared error, The annals of statistics, 20, 712-736, (1992) · Zbl 0746.62040
[10] Ronchetti, E., Optimal robust estimators for the concentration parameter of a von mises – fisher distribution, (), 65-74
[11] Silverman, B.W., Density estimation for statistics and data analysis, (1986), Chapman and Hall London · Zbl 0617.62042
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.