On the favorable estimation for fitting heavy tailed data

Stehlík, Milan; Potocký, Rastislav; Waldl, Helmut; Fabián, Zdeněk

doi:10.1007/s00180-010-0189-1

Cited by 51 publications

(29 citation statements)

References 12 publications

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“…Hence robust operators and procedures have to be implemented. To our best knowledge, for collective claims similar computations/simulations have not yet been made, especially novelty is the usage of the Christoph and Mikosch-Nagaev formula and their fi t. Discussing aggregated claims extends the results obtained in Stehlík, Potocký, Fabián, Waldl (2010).…”

Section: Discussionmentioning

confidence: 69%

“…Alexander, 2005) the maximum likelihood estimator of parameters failed to provide a reasonable estimation. Instead estimators based on Johnson moments should be used (see Stehlík, Potocký, Fabián, Waldl, 2010). More robust alternatives to MLE approach have been proposed by Juárez and Schucany (2004).…”

Section:  353mentioning

confidence: 99%

“…We have p-values for testing Pareto distribution with the according parameters: ML: 6.68e -5 unbiased ML: 7.01e -5 Johnson estimator: 4.84e -7 QQ: 7.01e -12, moment estimator: 2.62e -43. Testing is based on the exact likelihood ratio test of the homogeneity of Pareto distributions, which is derived in Stehlík, Potocký, Fabián and Waldl (2010) and used here as an omnibus test for Pareto distributions. From this test p-values are simulated in Matlab.…”

Section: An Application Of Christoph's Formulamentioning

confidence: 99%

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On Sums of Claims and their Applications in Analysis of Pension Funds and Insurance Products

Potocký¹,

Waldl²,

Stehlík³

2014

Prague Economic Papers

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Abstract:The problem that assets of a fund are not suffi cient to cover its liabilities is of extreme importance both for its members as well as for fund managers. We show that this problem can be solved via total claims distributions and give answers to the following questions: How much money will be needed in the fi rst pillar in order to satisfy the requirements of pensioners in a time horizon and which groups of working people should join also the second pillar because their benefi ts from it will be greater than those from the fi rst pillar? Though the paper concentrates primarily on the situation with Slovakian pension funds we believe that our fi ndings are more general. We show that the alternative methods should be used for calculation of extremes. We discuss the so-called barrier strategy for treating the surplus of an insurance company and bring some new results concerning it.

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Section: Discussionmentioning

confidence: 69%

Section:  353mentioning

confidence: 99%

Section: An Application Of Christoph's Formulamentioning

confidence: 99%

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On Sums of Claims and their Applications in Analysis of Pension Funds and Insurance Products

Potocký¹,

Waldl²,

Stehlík³

2014

Prague Economic Papers

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“…The maximum likelihood estimatorα ML,n := 1 H kn,n of Pareto tail index is very sensitive to deviations from the theoretical distributions, namely in the heavy-tailed class of distributions, see Stehlík et al (2010b). It is unbiased, asymptotically consistent and has smallest variance in the set of all unbiased estimators for α.…”

Section: Empirical Study Of the Effect Of Contamination On Pareto Taimentioning

confidence: 99%

“…In Fabián (2001) a new score method of score moment estimators has been proposed. It appeared that these score moment estimators are robust for very heavy tailed distributions, see Stehlík et al (2010a). Jordanova and Pancheva (2012) consider an independent identically distributed (i.i.d.)…”

Section: Introductionmentioning

confidence: 99%

Weak properties and robustness of t-Hill estimators

et al. 2016

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We describe a novel method of heavy tails estimation based on transformed score (t-score). Based on a new score moment method we derive the t-Hill estimator, which estimates the extreme value index of a distribution function with regularly varying tail. t-Hill estimator is distribution sensitive, thus it differs in e.g. Pareto and log-gamma case. Here, we study both forms of the estimator, i.e. t-Hill and t-lgHill. For both estimators we prove weak consistency in moving average settings as well as the asymptotic normality of t-lgHill estimator in iid setting. In cases of contamination with heavier tails than the tail of original sample, t-Hill outperforms several robust tail estimators, especially in small samples. A simulation study emphasizes the fact that the level of contamination is playing a crucial role. The larger the contamination, the better are the t-score moment estimates. The reason for this is the bounded t-score of heavy-tailed distributions (and, consequently, bounded influence functions of the estimators). We illustrate the developed methodology on a small sample data set of stake measurements from Guanaco glacier in Chile.

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