A moving window approach for nonparametric estimation of the conditional tail index

By Laurent Gardes, Stéphane Girard. 2008

84 citations recorded by the source corpus.

We present a nonparametric family of estimators for the tail index of a Pareto-type distribution when covariate information is available. Our estimators are based on a weighted sum of the log-spacings between some selected observations. This selection is achieved through a moving window approach on the covariate domain and a random threshold on the variable of interest. Asymptotic normality is proved under mild regularity conditions and illustrated for some weight functions. Finite sample performances are presented on a real data study.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5c0b43a5b3198cd12a563d0a39ec57fa7efdd0c1

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Citations in the corpus

Kernel estimators of extreme level curves (2011, background): “We refer to [19] for an heuristical solution.”
Nonparametric regression estimation of conditional tails: the random covariate case (2014, methodology): “[12] Gardes L, Girard S.”
Functional kernel estimators of large conditional quantiles (2011, methodology): “Nonparametric methods based on moving windows and nearest neighbors are introduced respectively in [25] and [26].”
Conditional extremes from heavy-tailed distributions: an application to the estimation of extreme rainfall return levels (2010, background): “We assume that for all x ∈ E, the conditional distribution function of Y is heavy-tailed, see also Gardes and Girard (2008).”
On kernel smoothing for extremal quantile regression (2012, unknown): “Recently, [14,16] proposed, respectively, a moving-window based estimator for the tail index and extreme quantiles of heavy-tailed conditional distributions, and they established their asymptotic properties.”
Estimation of the conditional tail index using a smoothed local Hill estimator (2014, methodology): “Fully non parametric methods have been considered using splines (see Chavez-Demoulin and Davison [4]), local polynomials (see Davison and Ramesh [6]), a moving window approach (see Gardes and Girard [8]), or a nearest neighbor approach (see Gardes and Girard [9]), among others.”
Evaluation of classical spatial-analysis schemes of extreme rainfall (2012, background): “As one very long series is more efficient than several shorter ones, numerous methods have been elaborated to gather in the same set rainfall series with common statistical properties ( Carreau and Girard, 2011; Cunnane, 1988; Daouia et al., 2011; Hosking and Wallis, 1997; Gardes and Girard, 2008; G”