Extreme value theory : an introduction

By Laurens de Haan, Ana Ferreira. 2006

2,915 citations recorded by the source corpus.

Subfields: Finance, Mechanical Engineering

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Citations in the corpus

Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approach (2018, methodology): “To efﬁciently and reliably estimate the local Lipschitz constant, we propose to use extreme value theory (De Haan & Ferreira, 2007) for robustness evaluation.”
On the block maxima method in extreme value theory: PWM estimators (2013, methodology): “This is an easily obtained variant of Theorem B.3.10 of de Haan and Ferreira (2006).”
Single-Model Uncertainties for Deep Learning (2018, methodology): “On the other hand, we would like to apply SQR to probabilistic forecasting [28], and extreme value theory [18].”
Geostatistics of extremes (2012, methodology): “The underlying mathematical basis is now thoroughly established (Leadbetter et al. 1983; Resnick 1987; Embrechts et al. 1997; de Haan & Ferreira 2006) and statistical tools and methods for use with a single time series of data, or with a few series, are well developed (Coles 2001; Beirlant et al.…”
Freezing and Decorated Poisson Point Processes (2014, background): “In this case, by classical results from extreme value theory [22] the limiting distribution of the recentered maximum is the Gumbel distribution.”
Bias correction in extreme value statistics with index around zero (2013, methodology): “The competitors are the moment quantile estimator x̂p,M introduced in Dekkers et al. (1989) and the PWM quantile estimator Student−t(3) Gumbel Note: Each sample consists of 5000 observations. γ̂ub is the bias-corrected PWM estimator in (3.10); γ̂pwm is the PWM estimator in (1.1); γ̂M is the moment e”
Non-Stationary Dependence Structures for Spatial Extremes (2014, background): “Since the supremum on the right-hand side of (2) could make Z(s) be degenerate at infinity, further technical conditions need to be imposed on W (s) (de Haan and Ferreira, 2006, §9.4).”
Time-Series Anomaly Detection Service at Microsoft (2019, background): “In 2017, SPOT and DSPOT [19] were proposed on the basis of Extreme Value Theory [6], the threshold of which can be selected automatically.”
Ultra-Reliable and Low-Latency Vehicular Transmission: An Extreme Value Theory Approach (2018, methodology): “To address this issue, we propose a solution based on EVT to locally characterize the distribution of the network-wide maximal queue length.”
An M-Estimator for Tail Dependence in Arbitrary Dimensions (2011, neutral): “…regular variation of the random vector (1/{1 − F1(X1j)})dj=1 on the cone [0,∞]d \ {(0, . . . ,0)} with limit measure or exponent measure µ given by µ({z ∈ [0,∞]d : z1 ≥ x1 or . . . or zd ≥ xd}) = l(1/x1, . . . ,1/xd) [Resnick (1987), Beirlant et al. (2004), de Haan and Ferreira (2006)].”
On kernel smoothing for extremal quantile regression (2012, background): “Next we extend the asymptotic normality far enough into the ‘most extreme’ order-β n regression quantiles with β n /α n → 0, thus providing a conditional analog of modern extreme-value results [19].”
Federated Learning in Mobile Edge Networks: A Comprehensive Survey (2019, background): “the authors in [179] propose the use of extreme value theory (EVT) [190].”