Abstract
In this work, we deal with a robust fitting of a wrapped normal model to multivariate circular data. Robust estimation is supposed to mitigate the adverse effects of outliers on inference. Furthermore, the use of a proper robust method leads to the definition of effective outlier detection rules. Robust fitting is achieved by a suitable modification of a classification-expectation-maximization algorithm that has been developed to perform a maximum likelihood estimation of the parameters of a multivariate wrapped normal distribution. The modification concerns the use of complete-data estimating equations that involve a set of data dependent weights aimed to downweight the effect of possible outliers. Several robust techniques are considered to define weights. The finite sample behavior of the resulting proposed methods is investigated by some numerical studies and real data examples.
Highlights
Multivariate Circular Data and Circular data arise commonly in many different fields such as earth sciences, meteorology, biology, physics, and protein bioinformatics
The purpose of robust estimation is twofold: On the one hand we aim to fit a model for the circular data at hand and on the other hand, an effective outlier detection rule can be derived from the robust estimation technique
We suggest a very general strategy that parallels the classical approaches to robust estimation of multivariate location and scatter under the common multivariate normal assumption, that can be extended to the more general setting of elliptical symmetric distributions
Summary
Multivariate Circular Data and Circular data arise commonly in many different fields such as earth sciences, meteorology, biology, physics, and protein bioinformatics. The purpose of robust estimation is twofold: On the one hand we aim to fit a model for the circular data at hand and on the other hand, an effective outlier detection rule can be derived from the robust estimation technique The latter often gives very important insight into the data generation scheme and statistical analysis. The key idea is that outlyingness is not measured directly on the torus as in [9] but only after unwrapping the multivariate circular data from the p-dimensional torus onto a hyperplane This approach allows one to search for outliers based on their geometric distance from the robust fit. The proposed robust estimation techniques lead to outlier detection strategies based on formal rules and the fitted model, by paralleling the classical results under a multivariate Normal model [15].
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