Heavy-Tail Phenomena: Probabilistic and Statistical Modeling

By Sidney I. Resnick. 2006

1,263 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/986ca9abbb6470b83703d5c86a5eea3adb010f41

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Citations in the corpus

Frontier estimation and extreme values theory (2010, unknown): “[17] and the references therein, Section 4.”
The harmonic moment tail index estimator: asymptotic distribution and robustness (2014, methodology): “Many distributions in applied fields such as hydrology, insurance or finance belong to the maximum domain of attraction of the Fréchet distribution which is characterized by heavy-tailed distributions (see e.g. Embrechts et al. 1997; Beirlant et al. 2004; Reiss and Thomas 2005; Resnick 2007).”
Multivariate peaks over thresholds models (2016, unknown): “This idea was introduced for multivariate extremes in Smith et al. (1997), and has since become a standard approach to inference.”
Towards estimating extremal serial dependence via the bootstrapped extremogram (2012, background): “Second, most bootstrapping applications in extreme value theory, even in the iid case, require the replicate time series to be of smaller order than the original sample size n; see e.g. Section 6.4 of Resnick [13].”
A discussion on mean excess plots (2009, methodology): “Other techniques are the Hill plot, the Pickands plot, the moment estimator plot and the QQ plot; cf. Chapter 4, Resnick (2007) and de Haan and Ferreira (2006).”
Asymptotics of random contractions (2010, methodology): “See Jessen and Mikosch (2006), Denisov and Zwart (2007), and Resnick (2007) for details on Breiman’s lemma and for some of its generalisations.”
Tail Risk of Multivariate Regular Variation (2011, background): “The examples and properties of MRV distributions, including the relation between MRV distributions and multivariate extreme value distributions with identical Fréchet margins can be found in [30, 31].”
Order Book Dynamics in Liquid Markets: Limit Theorems and Diffusion Approximations (2012, methodology): “The tail exponent β > 0 is diﬃcult to estimate precisely, but the Hill estimator Resnick (2006) can be used to measure the heaviness of the tails.”
Variational Inference with Tail-adaptive f-Divergence (2018, background): “To be concrete, a non-negative random variable w is called fat-tailed 2 (e.g., Resnick, 2007) if its tail probability ¯ F w ( t ) := Pr( w ≥ t ) is asymptotically equivalent to t − α ∗ as t → + for some ﬁnite positive number α ∗ (denoted by ¯ F w ( t ) ∼ t − α ∗ ), which means that where L is a…”
Stress scenario selection by empirical likelihood (2015, methodology): “A random variable X is regularly varying with index ν (RV(ν)) if the function → P(X ≥ ) is regularly varying with index −ν. Proposition 2.6 of Resnick (2007) shows that if h is regularly varying with index −ν < 0, then for any > 0 there exists K > 0 such that (1 − )x−ν− h( x) h( ) (1 + )x−ν+ (9)”
Power-Law Distributions in Empirical Data (2007, background): “Other estimators, however, can often yield more useful results—see, for example, Kratz and Resnick (1996) and Stoev et al. (2006).”
Conditioning on an extreme component: Model consistency with regular variation on cones (2008, methodology): “The technique is used in classical multivariate extreme value theory to characterize multivariate domains of attraction and dates back to at least [7]; see also [6,19,20,27] and [29], Chapter 5.”
Geostatistics of Dependent and Asymptotically Independent Extremes (2013, unknown): “An argument originally due to Fisher and Tippett (1928) and subsequently greatly extended (Leadbetter et al. 1983; Galambos 1987; Resnick 2006; de Haan and Ferreira 2006) shows that the suitably rescaled maxima of independent random variables, and of a wide variety of random processes, follow the…”
Extremal dependence of random scale constructions (2018, background): “Let g ( t ) = 1 − τ 1 ( b 1 − t ), which is decreasing as t → 0 and invertible, with (2007, Proposition 2.6(v)), adapting to regular variation at zero).”