Distribution and dependence-function estimation for bivariate extreme-value distributions

By Peter Hall, N. Tajvidi. 2000

126 citations recorded by the source corpus.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9acbe9928314ed8718ee8d4b80c122801a135da7

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Citations in the corpus

Extreme-value copulas (2009, methodology): “The estimator presented in [50] is given by Not only does the estimator’s construction guarantee that the endpoint conditions are veriﬁed, in addition it always veriﬁes the constraint ˆ A HT ( t ) > 1 ∨ ( 1 − t ) .”
Non‐parametric Estimation of Tail Dependence (2006, methodology): “In this context, non-parametric estimators have been proposed, e.g. in Abdous et al. (1999), Hall & Tajvidi (2000) and Falk & Reiss (2003).”
A dependence measure for multivariate and spatial extreme values: Properties and inference (2003, methodology): “For t=0, h@ A,t reduces to a variant of the Hall & Tajvidi (2000b) estimator that has been introduced to estimate the V function of a multivariate extreme-value distribution.”
Nonparametric estimation of the dependence function for a multivariate extreme value distribution (2008, methodology): “As in the case p = 2 studied by Hall and Tajvidi [10], one may expect that both Â(s1, .”
Likelihood estimators for multivariate extremes (2014, methodology): “Non-parametric estimation procedures have also been considered (see, e.g., Pickands 1981; Deheuvels and Tiago de Oliveira 1989; Deheuvels 1991; Smith et al. 1990; Capéraà et al. 1997; Hall and Tajvidi 2000; Boldi and Davison 2007), but in the present paper we focus on parametric approaches.”
A conditional approach for multivariate extreme values (with discussion) (2004, methodology): “…models for the multivariate extreme value distribution to describe componentwise maxima of Tawn (1988, 1990), Joe (1994), Capéraà et al. (1997) and Hall and Tajvidi (2000) and the multivariate threshold methods of Coles and Tawn (1991, 1994), Joe et al. (1992), de Haan and Resnick (1993), Sinha…”
Multivariate nonparametric estimation of the Pickands dependence function using Bernstein polynomials (2014, methodology): “g dependence) and 1 (independence). Table1compares four non-parametric estimators introduced in Section2: the madogram estimator (MD), thePickands (1981) estimator (P), the multivariate version of theHall and Tajvidi (2000) estimator (HT), and nally the multivariate extension of theCaperaa, Fougeres”
New estimators of the Pickands dependence function and a test for extreme-value dependence (2011, background): “ickands dependence functions. However, the literature provides many proposals on how to enforce these conditions. Various endpoint corrections have been proposed by Deheuvels (1991), Segers (2007) or Hall and Tajvidi (2000) among others. Fils-Villetard et al. (2008) 18 proposed an L2-projection of t”
Statistics of Extremes (2004, background): “Heffernan and Tawn (2004) develop a comparable approach in a general dvariate setting.”
Nonparametric estimation of multivariate extreme-value copulas (2011, methodology): “Similarly, for unknown margins, the multivariate extension of the estimator in Hall and Tajvidi (2000) simplifies tôAHTn (w) = Â P n(w)/Â P n(e j) = ÂPn(w){1+O(n −1 logn)}.”
A goodness-of-fit test for bivariate extreme-value copulas (2011, background): “When the margins are known, this phenomenon is well documented; see, for example, [4, 22] or [32].”
Joint probability of precipitation and discharge deficits in the Netherlands (2004, unknown): “Transforming again the original variables to standard uniform variables, the following nonparametric estimate of A(w) is obtained [Hall and Tajvidi, 2000]: Â wð Þ ¼ n Xn i¼1 Zi wð Þ " # 1 ; ð11Þ where Zi wð Þ ¼ min ln ui 1 wð Þln u ; ln vi wln v 0 w 1ð Þ; with (ui, vi) defined in equation (7) and…”
RANK-BASED INFERENCE FOR BIVARIATE EXTREME-VALUE COPULAS (2007, unknown): “(2.5) An alternative correction inspired by Hall and Tajvidi (2000) is given by 1/AHTn,r (t) = 1 n n ∑ i=1 ξ̄i(t), where for all t ∈ [0,1] and i ∈ {1, . . . , n}, ξ̄i(t) = S̄i 1− t ∧ T̄i t with S̄i = nŜi/(Ŝ1 + · · ·+ Ŝn) and T̄i = nT̂i/(T̂1 + · · ·+ T̂n).”