The problem of stability of mixtures of probability distributions to perturbations of mixing distributions is considered. Estimates of the distance between scale/location mixtures via the distance between the mixing distributions are obtained in terms of the Lévy–Prokhorov metric. Similar problems for scale or location mixtures are considered in terms of the Lévy metric. The results are formulated for normal mixtures. In conclusion, some algorithms are proposed for the construction of analogous estimates for other classes of mixtures.
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Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, Vol. 22, pp. 154–172, 2010
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Nazarov, A.L. On the Stability of Mixtures of Probability Distributions to Perturbations of Mixing Distributions. J Math Sci 267, 68–80 (2022). https://doi.org/10.1007/s10958-022-06117-y
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DOI: https://doi.org/10.1007/s10958-022-06117-y