Estimating the tail index

Csörgő, Sándor; Viharos, László

doi:10.1016/b978-044450083-0/50055-1

Cited by 45 publications

(31 citation statements)

References 83 publications

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“…It can be shown (see Lemma 2) that there exist no sequence (k n ) verifying condition (8), and thus, it is not possible to make the bias term vanish. This comparison is completed on Section 5 by some simulations.…”

Section: Comparison With Broniatowski Estimatormentioning

confidence: 99%

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A Hill Type Estimator of the Weibull Tail-Coefficient

Girard

2004

Communications in Statistics - Theory and Methods

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We present a new estimator of the Weibull tail-coefficient. The Weibull tail-coefficient is defined as the regular variation coefficient of the inverse cumulative hazard function. Our estimator is based on the log-spacings of the upper order statistics. Therefore, it is very similar to the Hill estimator for the extreme value index. We prove the weak consistency and the asymptotic normality of our estimator. Its asymptotic as well as its finite sample performances are compared to classical ones.

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Section: Comparison With Broniatowski Estimatormentioning

confidence: 99%

“…We refer to [8] for a review on this topic. Although estimators (1) and (2) do not address the same problem, it will appear that they share similar properties.…”

Section: Introductionmentioning

confidence: 99%

A Hill Type Estimator of the Weibull Tail-Coefficient

Girard

2004

Communications in Statistics - Theory and Methods

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“…We recall that this property is not shared by the Hill estimator (see e.g. Csörgő and Viharos (1998)). Moreover, the norming sequence is again the ideal factor k 1/2 n .…”

Section: −1mentioning

confidence: 99%

“…The problem of estimating R or other related tail indices, has received considerable attention and common applications may be found in a big variety of domains. For an overview of the subject, we refer to Csörgő and Viharos (1998). Following Csörgő and Steinebach (1991), we consider an important application in risk theory, namely the estimation of the adjustment coefficient.…”

Section: −1mentioning

confidence: 99%

Limiting behaviour of a geometric-type estimator for tail indices

Brito

Freitas

2003

Insurance: Mathematics and Economics

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Let Z 1 , Z 2 , ... be i.i.d. random variables with tail behaviour, where r is a regularly varying function at infinity and R is a positive constant. We consider the problem of estimating the exponential tail coefficient R, by methods mainly based on least squares considerations. Using a geometrical reasoning, we introduce a consistent estimator, whose values lay between the least squares estimates proposed by Schultze and Steinebach (1996). We investigate here the weak asymptotic properties of this geometrictype estimator, showing in particular that, under general conditions, its distribution is asymptotically normal. The results are applied to the related problem of estimating the adjustment coefficient in risk theory (Csörgő and Steinebach (1991)) and a simulation study is performed in order to illustrate the finite sample behaviour of this estimator.

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“…One of these estimators was also introduced by Kratz and Resnick (1996) in an independent but equivalent way. In general, when compared with other tail index estimators, it is reported that the estimators proposed by Schultze and Steinebach have a very good behaviour, with a better performance in several situations (see Csörgő and Viharos (1998)). Namely one of the interesting characteristics of the least squares estimators is the smoothness of the realizations as a function of k. It should be noted that the high variability that some tail estimators present makes more difficult the proper selection of the number of upper o.s.…”

Section: Bias-corrected Geometric-type Estimators Of the Tail Indexmentioning

confidence: 99%

Bias-corrected geometric-type estimators of the tail index

Brito

Cavalcante

Freitas

2016

J. Phys. A: Math. Theor.

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Abstract. The estimation of the tail index is a central topic in extreme value analysis. We consider a geometric-type estimator for the tail index and study its asymptotic properties. We propose here two asymptotic equivalent bias-corrected geometric-type estimators and establish the corresponding asymptotic behaviour. We also apply the suggested estimators to construct asymptotic confidence intervals for this tail parameter. Some simulations in order to illustrate the finite sample behaviour of the proposed estimators are provided.

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Estimating the tail index

Cited by 45 publications

References 83 publications

A Hill Type Estimator of the Weibull Tail-Coefficient

A Hill Type Estimator of the Weibull Tail-Coefficient

Limiting behaviour of a geometric-type estimator for tail indices

Bias-corrected geometric-type estimators of the tail index

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