Semiparametric Empirical Likelihood for Circular Distributions

A new family of circular distributions has been proposed as circular distributions generated from general spectral densities of time series models. These circular models have shown promising potential for analyzing and interpreting circular data. However, a significant challenge arises in the statistical inference for those circular data due to the loss of explicit forms associated with the normalizing constants in these circular models. We consider the empirical likelihood for data coming from these circular distributions. The proposed empirical likelihood ratio test has a chi-squared limiting distribution. The theoretical results are illustrated by numerical simulations and real data analysis.