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Robust Estimation in the Normal Mixture Model Based on Robust Clustering

J. A. Cuesta-Albertos, C. Matrán and A. Mayo-Iscar
Journal of the Royal Statistical Society. Series B (Statistical Methodology)
Vol. 70, No. 4 (Sep., 2008), pp. 779-802
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/20203855
Page Count: 24
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Robust Estimation in the Normal Mixture Model Based on Robust Clustering
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Abstract

We introduce a robust estimation procedure that is based on the choice of a representative trimmed subsample through an initial robust clustering procedure, and subsequent improvements based on maximum likelihood. To obtain the initial trimming we resort to the trimmed k-means, a simple procedure designed for finding the core of the clusters under appropriate configurations. By handling the trimmed data as censored, maximum likelihood estimation provides in each step the location and shape of the next trimming. Data-driven restrictions on the parameters, rquiring that every distribution in the mixture must be sufficiently represented in the initial clustered region, allow singularities to be avoided and guarantee the existence of the estimator. Our analysis includes robustness properties and asympotic results as well as worked examples.

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