Smoothed circulas: Nonparametric estimation of circular cumulative distribution functions and circulas
Jose Ameijeiras‐Alonso, Irène Gijbels · Bernoulli · 2024
Copulas are an important tool to study dependencies for data on the real line (or multivariate extensions of this), referred to as linear data. The analogue of copulas for circular data and data on the torus are circulas. This paper studies kernel estimation of circulas, and discusses important issues such as choice of circular kernels and ‘smoothing’ parameters. This leads to some new insights, and some contrasts with results for linear data. Since a circula is a multivariate cumulative distribution with circular uniform marginals, the paper also contributes to kernel estimation of cumulative distributions for toroidal data.