Abstract
A weighted likelihood technique for robust estimation of multivariate Wrapped distributions of data points scattered on a p-dimensional torus is proposed. The occurrence of outliers in the sample at hand can badly compromise inference for standard techniques such as maximum likelihood method. Therefore, there is the need to handle such model inadequacies in the fitting process by a robust technique and an effective downweighting of observations not following the assumed model. Furthermore, the employ of a robust method could help in situations of hidden and unexpected substructures in the data. Here, it is suggested to build a set of data-dependent weights based on the Pearson residuals and solve the corresponding weighted likelihood estimating equations. In particular, robust estimation is carried out by using a Classification EM algorithm whose M-step is enhanced by the computation of weights based on current parameters’ values. The finite sample behavior of the proposed method has been investigated by a Monte Carlo numerical study and real data examples.
Highlights
Multivariate circular observations arise commonly in all those fields where a quantity of interest is measured as a direction or when instruments such as compasses, protractors, weather vanes, sextants or theodolites are used [24]
Large values of the Pearson residual function correspond to regions of the support Y where the model fits the data poorly, meaning that the observation is unlikely to occur under the assumed model
Robust estimation is achieved by a suitable modification of their CEM algorithm, consisting in a weighting step before performing the M-step, in which data-dependent weights are evaluated according to (6) yielding a Weighted Likelihood Estimating Equation (WLEE) (8) to be solved in the M-step
Summary
Multivariate circular observations arise commonly in all those fields where a quantity of interest is measured as a direction or when instruments such as compasses, protractors, weather vanes, sextants or theodolites are used [24].
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