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A crucial aspect of threshold-based extreme value analyses is the level at which the threshold is set. For a suitably high threshold asymptotic theory suggests that threshold excesses may be modelled by a generalized Pareto distribution. A common threshold diagnostic is a plot of estimates of the generalized Pareto shape parameter over a range of thresholds. The aim is to select the lowest threshold...
Summary. For extreme value modelling based on threshold techniques, a well‐documented issue is the sensitivity of inference from the model to the choice of threshold. The threshold above which we assume a non‐homogeneous Poisson process, or equivalently generalized Pareto representation, to be a reasonable approximation to the distribution is traditionally selected before analysis and subsequently...
In the family of distribution functions with nondegenerate right tail, we test the hypothesis $$H_{m_0 } $$ with a hypothetical m0 > 0 and with some x0 ≥ 0. The proposed test is fully nonparametric and is based on splitting the set of observations into N subsamples of size n and on the empirical distribution function of the extremes of the subsamples; the asymptotics...
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