On posterior consistency of tail index for Bayesian kernel mixture models. (English) Zbl 1466.62268

Summary: Asymptotic theory of tail index estimation has been studied extensively in the frequentist literature on extreme values, but rarely in the Bayesian context. We investigate whether popular Bayesian kernel mixture models are able to support heavy tailed distributions and consistently estimate the tail index. We show that posterior inconsistency in tail index is surprisingly common for both parametric and nonparametric mixture models. We then present a set of sufficient conditions under which posterior consistency in tail index can be achieved, and verify these conditions for Pareto mixture models under general mixing priors.


62F15 Bayesian inference
62G32 Statistics of extreme values; tail inference
62H30 Classification and discrimination; cluster analysis (statistical aspects)


BNPdensity; plfit
Full Text: DOI arXiv Euclid


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