Permutation bootstrap and the block maxima method

Mefleh, Aline; Biard, Romain; Dombry, Clément; Khraibani, Zaher

doi:10.1080/03610918.2018.1563146

Cited by 3 publications

(2 citation statements)

References 19 publications

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“…However, for all existing BM estimators, based on either disjoint or sliding blocks, permutating the observations will in general not lead to the same estimate of γ. Based on this fact, Mefleh et al (2019) construct a permutation bootstrap method for reducing the estimation uncertainty in estimators from the BM approach.…”

Section: Introductionmentioning

confidence: 99%

All Block Maxima method for estimating the extreme value index

Oorschot,

Zhou

2020

Preprint

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The block maxima (BM) approach in extreme value analysis fits a sample of block maxima to the Generalized Extreme Value (GEV) distribution. We consider all potential blocks from a sample, which leads to the All Block Maxima (ABM) estimator. Different from existing estimators based on the BM approach, the ABM estimator is permutation invariant. We show the asymptotic behavior of the ABM estimator, which has the lowest asymptotic variance among all estimators using the BM approach. Simulation studies justify our asymptotic theories. A key step in establishing the asymptotic theory for the ABM estimator is to obtain asymptotic expansions for the tail empirical process based on higher order statistics with weights.

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Section: Introductionmentioning

confidence: 99%

All Block Maxima method for estimating the extreme value index

Oorschot,

Zhou

2020

Preprint

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“…In our analysis, we used bootstrap methods, introduced by Efron [1], to understand the structure of the data and to construct confidence intervals for the estimations. Besides classical bootstrap and permutation bootstrap for extreme values [15], we have also used parametric bootstrap [12]. Resampling methods can be used for construction confidence intervals for trend coefficient under different models.…”

Section: Introductionmentioning

confidence: 99%

Trend detection in GEV models

Németh,

Hübnerová,

Zempléni

2019

Preprint

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In recent environmental studies extreme events have a great impact. The yearly and monthly maxima of environment related indices can be analysed by the tools of extreme value theory. For instance, the monthly maxima of the fire weather index in British Columbian forests might be modelled by GEV distribution, but the stationarity of the time series is questionable. This property can lead us to different approaches to test if there is a significant trend in past few years data or not. An approach is a likelihood ratio based procedure which has favourable asymptotic properties, but for realistic sample sizes it might have a large error. In this paper we analyse the properties of the likelihood ratio test for extremes by bootstrap simulations and aim to determine a minimal required sample size. With the theoretical results we re-asses the trends of fire weather index in British Columbian forests.

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