On maximum likelihood estimation of the extreme value index

By H. Drees, Ana Ferreira, Laurens de Haan. 2004

141 citations recorded by the source corpus.

textabstractWe prove asymptotic normality of the so-called maximum likelihood estimator of the extreme value index.

Subfields: Finance, Management of Technology and Innovation, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/090d2d2b11c2f8a3fdb8445ec1640db0a1e159c6

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Citations in the corpus

Approximations to the tail empirical distribution function with application to testing extreme value conditions (2006, methodology): “In Theorem 2.1 of Drees et al. (2003) it is proved that γ̂n, â(n/kn) := σ̂n and b̂(n/kn) := Xn−kn,n satisfy (2.6) with Γ(Wn) = −(γ + 1) 2 γ ( (2γ + 1)Sn −Rn ) + (γ + 1)Wn(1), α(Wn) = −γ + 1 γ ( Rn − (γ + 1)(2γ + 1)Sn )− (γ + 2)Wn(1), β(Wn) = Wn(1), where Rn := ∫ 1 0 t−1Wn(t) dt, Sn := ∫ 1 0…”
On an extreme value version of the Birnbaum-Saunders distribution (2012, methodology): “We refer the peaks over threshold methodology of estimation (see Smith, 1987) as well as the methodology used by Drees et al. (2004), named peaks over random threshold in Araújo Santos et al. (2006).”
Second-order refined peaks-over-threshold modelling for heavy-tailed distributions (2009, background): “Its asymptotics have been studied in Smith (1987), Drees et al. (2004) and de Haan and Ferreira (2006, Theorem 3.4.2).”
On the maximum likelihood estimator for the Generalized Extreme-Value distribution (2016, methodology): “An interesting side result concerns the differentiability in quadratic mean of that family; for the Gumbel case, see Marohn (1994, 2000). As in Smith (1985), we need to show that certain limit relations hold uniformly over specific subsets of the parameter space. To do so, we use empirical process m”
Hidden regular variation and the rank transform (2005, background): “(See also Beirlant and Vandewalle (2002), Drees et al. (2004), and Peng (1999).)”
Estimation of the extreme-value index and generalized quantile plots (2005, unknown): “…ªþ 1) (1 3ª)(1 4ª)k þ 1 2ª ~r(1 ~r) b n k 2 , if r 2 ª , 0, (1 ª)2(1 2ª)(6ª2 ªþ 1) (1 3ª)(1 4ª)k þ (1 2ª) (1 ª)(1 3ª) A(1 ª)2 2‘þ=U (1) A(1 ª) ‘þ=U (1) b n k 2 , if ª ¼ r: 8>>>>>>>>>>>>< >>>>>>>>>>>>: Drees et al. (2004) stated the following expressions for the AMSE of for the…”
ON TAIL INDEX ESTIMATION FOR DEPENDENT, HETEROGENEOUS DATA (2010, background): “Further, it is easy to show the third term in (26) satises for all u 2 R (27) m n ln X(mn+1) bmn = u () 1 1 m 1=2 n n X”
Bivariate tail estimation: dependence in asymptotic independence (2004, methodology): “Now can be estimated by the maximum likelihood estimator ̂1 in a generalized Pareto model, based on the largest mþ 1 order statistics of the T (n)i (cf. Drees et al. 2004); here m ¼ m(n) denotes an intermediate sequence, that is, m !”
On testing extreme value conditions (2006, methodology): “In that paper the exact formulas of Lγ and Tγ are given for the maximum likelihood estimates (e.g., see Smith (1985) and Drees et al. (2004)), which depend only on γ and η.”