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Influence measures and robust estimators of dependence in multivariate extremes. (English) Zbl 1329.62148

Summary: We develop a simple influence measure to assess whether Bayesian estimators in multivariate extreme value problems are sensitive to outliers. The proposed measure is easy to compute by importance sampling and successfully captures two effects on the functional: the “data effect” and the “parameter uncertainty effect”. We also propose a new Bayesian estimator which is easy to implement and is robust. The methods are tested and illustrated using simulated data and then applied to stock market data.

MSC:

62F15 Bayesian inference
62G32 Statistics of extreme values; tail inference
62G35 Nonparametric robustness
62P05 Applications of statistics to actuarial sciences and financial mathematics

Software:

BayesDA
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References:

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