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On tail parameter estimation in certain point process models
Institution:Institut für Mathematische Stochastik, Universität Freiburg, Hebelstr, 27, D-79104 Freiburg im Breisgau, Germany
Abstract:Let μ(ds, dx) denote Poisson random measure with intensity dsG(dx) on (0, ∞) × (0, ∞), for a measure G(dx) with tails varying regularly at ∞. We deal with estimation of index of regular variation α and weight parameter ξ if the point process is observed in certain windows Kn = 0, Tn] × Yn, ∞), where Yn → ∞ as n → ∞. In particular, we look at asymptotic behaviour of the Hill estimator for α. In certain submodels, better estimators are available; they converge at higher speed and have a strong optimality property. This is deduced from the parametric case G(dx) = ξαxα−1 dx via a neighbourhood argument in terms of Hellinger distances.
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