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Mixtures of distributions: Inference and estimation. (English) Zbl 0849.62013
Gilks, W. R. (ed.) et al., Markov chain Monte Carlo in practice. London: Chapman & Hall. 441-464 (1996).
Mixtures of distributions can model quite exotic distributions with few parameters and a high degree of accuracy. In our opinion, they are satisfactory competitors to more sophisticated methods of nonparametric estimation, in terms of both accuracy and inferential structure. Even when the mixture components do not allow for a model-related interpretation, the various parameters appearing in the final combination are still much easier to assess than coefficients of a spline regression, local neighbourhood sizes of a histogram density estimate, or location-scale factors of a wavelet approximation. Moreover, subsequent inferences about the modelled phenomenon are quite simple to derive from the original components of the mixture, since these distributions have been chosen for their tractability.
62F10Point estimation
62G05Nonparametric estimation