RANK-BASED INFERENCE FOR BIVARIATE EXTREME-VALUE COPULAS

By Christian Genest, Johan Segers. 2007

153 citations recorded by the source corpus.

Consider a continuous random pair (X, Y ) whose dependence is characterized by an extreme-value copula with Pickands dependence function A. When the marginal distributions of X and Y are known, several consistent estimators of A are available. Most of them are variants of the estimators due to Pickands [Bull. Inst. Internat. Statist. 49 (1981) 859–878] and Cap´era`a, Foug`eres and Genest [Biometrika 84 (1997) 567–577]. In this paper, rank-based versions of these estimators are proposed for the more common case where the margins of X and Y are unknown. Results on the limit behavior of a class of weighted bivariate empirical processes are used to show the consistency and asymptotic normality of these rank-based estimators. Their finite- and large-sample performance is then compared to that of their known-margin analogues, as well as with endpoint-corrected versions thereof. Explicit formulas and consistent estimates for their asymptotic variances are also suggested

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7d4915fc98d140542c33ef32fa6f38f76321dbf0

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Citations in the corpus

Multivariate multiparameter extreme value models and return periods: A copula approach (2010, methodology): “Since A can be estimated via empirical data [Genest and Segers, 2009], then it may be used to check the statistical adequacy of different models.”
A comparative copula‐based bivariate frequency analysis of observed and simulated storm events: A case study on Bartlett‐Lewis modeled rainfall (2011, background): “A bivariate extreme value distribution could be of interest when an association between the maxima of two random variables is suspected [see, e.g., Tawn, 1998; Genest and Segers, 2009, and references therein].”
A Horse Race between the Block Maxima Method and the Peak–over–Threshold Approach (2018, background): “…are estimated nonparametrically; see Bücher (2014) for a discussion of the empirical stable tail dependence function from Section 4.1 below, and Genest and Segers (2009) for estimation of Pickands dependence function based on i.i.d. data from a bivariate extreme value distribution, Section…”
An Overview of the Goodness-of-Fit Test Problem for Copulas (2012, methodology): “independent from margins, by invoking empirical counterparts of the Pickands function introduced in [47]: given our previous notations,”
Extreme-value copulas (2009, result): “In [37], asymptotic results were established under much weaker conditions.”
Nonparametric estimation of multivariate extreme-value copulas (2011, methodology): “Explanations on the construction of these estimators are provided for instance in the original references given before, in Genest and Segers (2009) and in the survey paper Gud ndorf and Segers (2010).”
Asymptotics of empirical copula processes under non-restrictive smoothness assumptions (2010, background): “For instance, the empirical copula is a basic building block when estimating copula densities (Chen and Huang [3], Omelka, Gijbels and Veraverbeke [22]) or dependence measures and functions (Schmid et al. [27], Genest and Segers [14]), for testing for independence (Genest and Rémillard [12], Genest,”
Multivariate nonparametric estimation of the Pickands dependence function using Bernstein polynomials (2014, background): “s reason, several nonparametric estimators of the Pickands dependence function have been proposed: see for instancePickands (1981), Caperaa et al. (1997),Hall and Tajvidi (2000),Zhang et al. (2008),Genest and Segers (2009),Buc her et al. (2011),Gudendorf and Segers(2011,2012), andBerghaus et al. (20”
A goodness-of-fit test for bivariate extreme-value copulas (2011, methodology): “Appendix C: Proof of Proposition 2 The proof closely mimics the argument presented in [19], Appendix B.”
On the Ghoudi, Khoudraji, and Rivest test for extreme‐value dependence (2009, background): “See Abdous & Ghoudi (2005) for a survey and FilsVilletard, Guillou & Segers (2008), Guillotte & Perron (2008) and Genest & Segers (2009) for more recent contributions.”
Flood Coincidence Risk Analysis Using Multivariate Copula Functions (2012, methodology): “5 and 6 as circles were calculated using the method proposed by Genest and Segers (2009). The fitted Pickand's function for all pairs of stations and three copula models of flood magnitudes in the two basins are plotted in Figs.”
New estimators of the Pickands dependence function and a test for extreme-value dependence (2011, methodology): “(a) If the marginals of (X,Y ) are independent the distribution of the random variable AΠ,h0 coincides with the distribution of the random variable Ar = − ∫ 1 0 GΠ(y 1−t, yt)y−1 dy, which appears as the weak limit of the appropriately standardized Pickands estimator; see Genest and Segers (2009). In”
A review of copula models for economic time series (2012, methodology): “[69] for Archimedean copulas, and by Genest and Segers [74] for extreme value copulas.”