Robust Estimation for Multivariate Wrapped Models

TL;DR

This paper introduces a robust weighted likelihood approach for estimating multivariate Wrapped Normal distributions on a torus, effectively handling outliers and hidden substructures in complex data.

Contribution

It proposes a novel robust estimation method using a Classification EM algorithm with data-dependent weights for multivariate wrapped models.

Findings

Method performs well in Monte Carlo simulations.

Effective in identifying outliers and substructures.

Demonstrated on real data examples.

Abstract

A weighted likelihood technique for robust estimation of a multivariate Wrapped Normal distribution for 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 down-weighting 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 studies and real data examples.