Robust Mixture Modeling using Weighted Complete Estimating Equations
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Mixture modeling that takes account of potential heterogeneity in data is widely adopted for classification and clustering problems. However, it can be sensitive to outliers especially when the mixture components are Gaussian. In this paper, we introduce the robust estimating methods using the weighted complete estimating equations for robust fitting of multivariate mixture models. The proposed approach is based on a simple modification of the complete estimating equation given the latent variables for grouping indicators with the weights that depend on the components of mixture distributions for downweighting outliers. We develop a simple expectation-estimating-equation (EEE) algorithm to solve the weighted complete estimating equations. As examples, the multivariate Gaussian mixture, mixture of experts and multivariate skew normal mixture are considered. In particular, we derive a novel EEE algorithm for the skew normal mixture which results in the closed form expressions for both the E- and EE-steps by slightly extending the proposed method. The numerical performance of the proposed method is examined through the simulated and real datasets.
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