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We consider robust estimation of wrapped models to multivariate circular datathat are points on the surface of a $p$-torus based on the weighted likelihoodmethodology.Robust model fitting is achieved by a set of weighted likelihoodestimating equations, based on the computation of data dependent weights aimedto down-weight anomalous values, such as unexpected directions that do notshare the main pattern of the bulk of the data. Weighted likelihood estimatingequations with weights evaluated on the torus orobtained after unwrapping thedata onto the Euclidean space are proposed and compared. Asymptotic propertiesand robustness features of the estimators under study have been studied,whereas their finite sample behavior has been investigated by Monte Carlonumerical experiment and real data examples.

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