Circular Discrete Reapproximation

We present a novel nonparametric scheme for modeling circular random variables. For that, the circular Cramer-von Mises distance (CCvMD) is proposed to measure the statistical divergence between two circular discrete models based on a smooth characterization of the localized cumulative distribution. Given a set of weighted samples from empirical data, the under-lying unknown distribution is then reapproximated by another sample set of configurable size and dispersion-adaptive layout in the sense of least CCvMD. Built upon the proposed circular discrete reapproximation (CDR), a new method is introduced for density estimation with von Mises mixtures. Moreover, the CDR scheme is extended to topological spaces composing the unit circle and Euclidean space of arbitrary dimension, and a new regression model for random circular vector fields is proposed based thereon. We provide case studies using synthetic and real-world data from wind climatology. Numerical results validate the efficacy of proposed approaches with promising potential of outperforming competitive methods.