Inference for the limiting cluster size distribution of extreme values

By Christian-Yann Robert. 2008

51 citations recorded by the source corpus.

Any limiting point process for the time normalized exceedances of high levels by a stationary sequence is necessarily compound Poisson under appropriate long range dependence conditions. Typically exceedances appear in clusters. The underlying Poisson points represent the cluster positions and the multiplicities correspond to the cluster sizes. In the present paper we introduce estimators of the limiting cluster size probabilities, which are constructed through a recursive algorithm. We derive estimators of the extremal index which plays a key role in determining the intensity of cluster positions. We study the asymptotic properties of the estimators and investigate their finite sample behavior on simulated data.

Subfields: Finance, Global and Planetary Change, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e56e6e051605b50b405323e15e48ecb410809c6d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Axel Bucher
2. Chen Zhou
3. Paul Northrop
4. Johan Segers
5. A. C. Davison
6. Jean-David Fermanian

In Global and Planetary Change

1. Chen Zhou
2. Axel Bucher
3. Paul Northrop
4. A. C. Davison

In Statistics and Probability

1. Chen Zhou
2. Axel Bucher
3. Paul Northrop
4. Johan Segers
5. Jean-David Fermanian

Citations in the corpus

• An efficient semiparametric maxima estimator of the extremal index (2015, methodology): “The blocks estimator (sometimes called the logs estimator) θ̂B = log Ĝ(u)/b log F̂ (u) (Smith and Weissman, 1994) requires the choice of a threshold u and a block size b. Robert (2009) extends this idea by using a random threshold, set at a particular sample quantile.”
• A sliding blocks estimator for the extremal index (2008, unknown): “The asymptotic variance of the disjoint blocks estimator corresponds with the one for the same estimator but at a random threshold (order statistic) in (16), Corollary 4.”
• A Horse Race between the Block Maxima Method and the Peak–over–Threshold Approach (2018, background): “…that rely on threshold exceedances (Ferro and Segers, 2003; Süveges, 2007), 3) estimators that use both principles simultaneously (Hsing, 1993; Robert, 2009; Robert, Segers and Ferro, 2009) and 4) estimators which, next to choosing a threshold sequence, require the choice of a run-length…”