Parameter estimation via Indirect Inference for multivariate Wrapped Normal distributions

Multivariate circular observations, i.e. points on a p-dimensional torus, can be seen as random angular quantities. A way to model this kind of observation is using the multivariate wrapped normal distribution. In this paper, we tackle the problem of estimating the multivariate wrapped normal distribution parameters using a given set of samples. Here we focus on the parameters in the variance-covariance matrix that characterize the dependence among the variables of interest. For this purpose, we propose an Indirect Inference approach that relies on a Normal auxiliary model defined on the real space with the same dimension as the target model’s parameter space. This approach provides an efficient and accurate estimation method for the parameters of the multivariate wrapped normal distribution.