Bias reduction of a tail index estimator through an external estimation of the second-order parameter

Gomes, M. Ivette; Caeiro, Frederico; Figueiredo, Fernanda

doi:10.1080/02331880412331284304

Cited by 41 publications

(43 citation statements)

References 16 publications

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“…However, the second-order parameter ρ(t) is unknown in practice making difficult the comparison of asymptotic bias associated to different log-gamma weights. We refer to [20,21] for estimators of the second-order parameter in the unconditional case. To overcome this problem, one can define the mean-squared bias as:…”

Section: Asymptotic Resultsmentioning

confidence: 99%

Conditional extremes from heavy-tailed distributions: an application to the estimation of extreme rainfall return levels

Gardès

Girard²

2010

Extremes

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− This paper is dedicated to the estimation of extreme quantiles and tail index from heavy-tailed distributions when a covariate is recorded simultaneously with the quantity of interest. A nearest neighbor approach is used to construct our estimators. Their asymptotic normality is established under mild regularity conditions. An application to the estimation of return periods of extreme rainfalls in the Cévennes-Vivarais region is provided.

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Section: Asymptotic Resultsmentioning

confidence: 99%

Conditional extremes from heavy-tailed distributions: an application to the estimation of extreme rainfall return levels

Gardès

Girard²

2010

Extremes

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“…stability criterion, like the 'largest run' suggested in refs. [9,16]. The relative behavior of the sample paths of M and M estimators immediately suggests the choice of the threshold k 10 in equation (17).…”

Section: Case Studiesmentioning

confidence: 99%

“…[14,15], Gomes et al [11] have considered, for a suitable ρ-estimator, ρ, the β-estimator β(k; ρ) in equation (9) and also computed at an intermediate level k 1 higher than k. The estimate β := β(k 1 ; ρ) is then incorporated in M(k; ρ), and it is there suggested the consideration of the estimator…”

Section: Second-order Reduced Bias Extreme Value Index Estimatorsmentioning

confidence: 99%

A heuristic adaptive choice of the threshold for bias-corrected Hill estimators

Gomes

Henriques‐Rodrigues

Vandewalle

et al. 2008

Journal of Statistical Computation and Simulation

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We shall deal with specific classes of the second-order reduced bias extreme value index estimators, devised for heavy tails. In those classes, the second-order parameters in the bias are estimated at a level k 1 of a larger order than that of the level k at which we compute the extreme value index estimator, and by doing this, it is possible to keep the asymptotic variance of the new estimators equal to the asymptotic variance of the Hill estimator, the maximum-likelihood estimator of the extreme value index γ , under a strict Pareto model. On the basis of an adequate pair of this type of extreme value index estimators, we also provide a heuristic adaptive choice of the threshold in reduced bias estimation and we proceed to an intensive computer simulation that enables us to study, through Monte-Carlo techniques, the behavior of the non-adaptive and adaptive proposed estimators. An illustration of the behavior of these estimators for sets of real data in the fields of finance and insurance is also provided.

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“…Gomes and Figueiredo (2006) suggest the use, in (7), of reduced-bias tail index estimators, like the ones in Martins (2001, 2002) and Gomes et al (2004), all with σ R > 1 in (13), being then able to reduce also the dominant component of the classical quantile estimator's asymptotic bias.…”

Section: Introductionmentioning

confidence: 98%