Selecting the optimal sample fraction in univariate extreme value estimation

Drees, Holger; Kaufmann, Edgar

doi:10.1016/s0304-4149(98)00017-9

Cited by 210 publications

(158 citation statements)

References 19 publications

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“…Once this has been done, the only remaining choice is that of the significance level of the test. Such choices are needed in all procedures to select the number of the order statistics to use (recall the subsample size in the bootstrap procedure of Danielsson et al (2001), or the threshold sequence of Drees and Kaufmann (1998)). We suggest a canonical way of choosing this significance level that appears to work reasonably well in the situations we have tried.…”

Section: The Estimation Proceduresmentioning

confidence: 99%

“…We compare the resulting performance of the estimator with the bootstrap procedure of Danielsson et al (2001) , the optimal sample fraction choice of Drees and Kaufmann (1998), and to the original testing procedure of Hill (1975). For the test data we choose i.i.d.…”

Section: Testing the Estimator On Simulated Datamentioning

confidence: 99%

“…• The optimal sample fraction choicek opt of Drees and Kaufmann (1998) with the initialβ n based on the upper 2 √ n order statistics, r n = 2.5β n n .25 , ψ = .7 and ρ 0 = 1.…”

Section: Testing the Estimator On Simulated Datamentioning

confidence: 99%

“…This method was later refined by Danielsson et al (2001) who suggested a two-level bootstrap procedure that works under minimal a priori available information. An alternative approach of finding this asymptotically optimal number k of upper order statistics was suggested, under slightly more restrictive assumptions, by Drees and Kaufmann (1998).…”

Section: Introductionmentioning

confidence: 99%

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Tail inference: where does the tail begin?

Nguyen

Samorodnitsky

2011

Extremes

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Abstract. The quality of estimation of tail parameters, such as tail index in the univariate case, or the spectral measure in the multivariate case, depends crucially on the part of the sample included in the estimation. A simple approach involving sequential statistical testing is proposed in order to choose this part of the sample. This method can be used both in the univariate and multivariate cases. It is computationally efficient, and can be easily automated. No visual inspection of the data is required. We establish consistency of the Hill estimator when used in conjunction with the proposed method, as well describe its asymptotic fluctuations. We compare our method to existing methods in univariate and multivariate tail estimation, and use it to analyze Danish fire insurance data.

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Section: The Estimation Proceduresmentioning

confidence: 99%

Section: Testing the Estimator On Simulated Datamentioning

confidence: 99%

“…• The optimal sample fraction choicek opt of Drees and Kaufmann (1998) with the initialβ n based on the upper 2 √ n order statistics, r n = 2.5β n n .25 , ψ = .7 and ρ 0 = 1.…”

Section: Testing the Estimator On Simulated Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Tail inference: where does the tail begin?

Nguyen

Samorodnitsky

2011

Extremes

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show abstract

“…The first aims to find the optimal cutoff point that balances the bias and variance assuming that the bias term in the asymptotic distribution is finite; see e.g. [3,8] and [12]. The second type corrects the bias under allowing that the bias term in the asymptotic distribution is at an infinite level; see e.g.…”

Section: Introductionmentioning

confidence: 99%

Adapting extreme value statistics to financial time series: dealing with bias and serial dependence

2016

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We handle two major issues in applying extreme value analysis to financial time series, bias and serial dependence, jointly. This is achieved by studying bias correction methods when observations exhibit weak serial dependence, in the sense that they come from β-mixing series. For estimating the extreme value index, we propose an asymptotically unbiased estimator and prove its asymptotic normality under the β-mixing condition. The bias correction procedure and the dependence structure have a joint impact on the asymptotic variance of the estimator. Then we construct an asymptotically unbiased estimator of high quantiles. We apply the new method to estimate the value-at-risk of the daily return on the Dow Jones Industrial Average index.

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Exceedance Over Threshold

Drees

2001

Encyclopedia of Environmetrics

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We discuss how to fit threshold models to the exceedances over high thresholds. In a univariate setting, often the crucial step is to estimate the extreme value index, since the accuracy achieved there essentially determines the estimation error for extreme quantiles or exceedance probabilities. In this context, the choice of the sample fraction used for estimation is particularly important. Besides classical models with independent and identically distributed observations, it is also discussed how to cope with serial dependence, trends and seasonality. When fitting a multivariate threshold model, one has to estimate whole functions that describe the tail dependence structure. Here mainly semiparametric and nonparametric estimators for the stable tail dependence function, the exponent measure and the angular measure are considered. In addition, we briefly study the problem of testing for asymptotic independence of the marginals. Finally, we touch on software specially designed for tail analysis.

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Selecting the optimal sample fraction in univariate extreme value estimation

Cited by 210 publications

References 19 publications

Tail inference: where does the tail begin?

Tail inference: where does the tail begin?

Adapting extreme value statistics to financial time series: dealing with bias and serial dependence

Exceedance Over Threshold

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