Weighted likelihood methods for robust fitting of wrapped models for $p$-torus data

We consider robust estimation of wrapped models to multivariate circular data that are points on the surface of a $p$-torus based on the weighted likelihood methodology.Robust model fitting is achieved by a set of weighted likelihood estimating equations, based on the computation of data dependent weights aimed to down-weight anomalous values, such as unexpected directions that do not share the main pattern of the bulk of the data. Weighted likelihood estimating equations with weights evaluated on the torus orobtained after unwrapping the data onto the Euclidean space are proposed and compared. Asymptotic properties and robustness features of the estimators under study have been studied, whereas their finite sample behavior has been investigated by Monte Carlo numerical experiment and real data examples.