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Minimum Hellinger distance estimation for finite mixture models. (English) Zbl 0881.62035

Summary: Minimum Hellinger distance estimates are considered for finite mixture models when the exact forms of the component densities are unknown in detail but are thought to be close to members of some parametric family. Minimum Hellinger distance estimates are asymptotically efficient if the data come from a member of the parametric family and are robust to certain departures from the parametric family. A new algorithm is introduced that is similar to the EM algorithm, and a specialized adaptive density estimate is also introduced. Standard measures of robustness are discussed, and some difficulties are noted. The robustness and asymptotic efficiency of the estimators are illustrated using simulations.

MSC:

62G05 Nonparametric estimation
62G07 Density estimation
62G35 Nonparametric robustness
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