Automatic bandwidth selection for circular density estimation

Charles C. Taylor

Given angular data $\theta_1,\ldots, \theta_n \in [0,2\pi)$ a common objective is to estimate the density. In the case that a kernel estimator is used, bandwidth selection is crucial to the performance. This paper obtains a `plug-in rule' for the bandwidth, which is based on the concentration of a reference density, namely, the von Mises distribution. It is seen that this is equivalent to the usual Euclidean plug-in rule in the case that the concentration becomes large. In the 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.

Keywords: Angle data; Kernel density estimators; von Mises distribution; Smoothing parameter selection.