Nonparametric estimating equations for circular probability density functions and their derivatives (Q1684139)

Circular data occur when the sample space is described by a circle, as opposed to the real line in standard statistics. Estimating equations for circular density estimation (and its derivatives), where local versions of population trigonometric moments are equated with their empirical counterparts, are proposed. Modelling via longer series will give smaller asymptotic bias without asymptotic variance inflation. The system is linear and has a closed-form solution, so the proposed estimators have a general formulation depending on both expansion degree and the order of the target derivative. This article also contains some theory for the case of dependent data. Theoretical results along with simulation experiments are provided.