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Abstract:
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A general class of robust weighted likelihood estimators (WLE) are considered for finite normal mixture model. For general density function models, the WLE class unifies several families of minimum disparity estimators through weighting function and bias adjustment terms, with influence function and asymptotic covariance matrix derived. A simple EM-like algorithm is described for finite normal mixture model. Three particular WLEs, corresponding to the density power divergence, symmetric chi-square and negative exponential disparity, are compared in a simulation study of three-component mixtures with substantially overlapping components and large contaminations. Results show that WLEs with weights based on kernel-smoothed Pearson residuals display more robustness than density power divergence or maximum likelihood estimators. A real data example is also provided.
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