Small sample estimation and testing for heavy tails

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62156489%3A43110%2F12%3A00183111" target="_blank" >RIV/62156489:43110/12:00183111 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/67985807:_____/12:00390574

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Small sample estimation and testing for heavy tails

Popis výsledku v původním jazyce

The aim of the paper is to introduce the distribution sensitive tail estimation procedure, which is easy to implement for various distributions. Here we construct distribution-sensitive estimators based on the Hills procedure using score moment estimators for other heavy-tailed distributions (Pareto, Fréchet, Burr, log-gama, inverse gamma, etc.), and to study their statistical properties, both theoretically (e.g consistency, asymptotical distribution) and by means of simulation experiments (e.g. comparisons of exact effectiveness of our method for different heavy tailed distributions). A specific problem is finding of an optimal threshold k, say, yielding a trade off in between of variance and bias of the Hill estimator. Simulation results by Embrechtset al. (1997) showed that the Hill estimator and its alternatives work well over large ranges of values for k in the case of Pareto distribution. However, Hill estimator is often giving wrong results for distributions different from the

Název v anglickém jazyce

Small sample estimation and testing for heavy tails

Popis výsledku anglicky

The aim of the paper is to introduce the distribution sensitive tail estimation procedure, which is easy to implement for various distributions. Here we construct distribution-sensitive estimators based on the Hills procedure using score moment estimators for other heavy-tailed distributions (Pareto, Fréchet, Burr, log-gama, inverse gamma, etc.), and to study their statistical properties, both theoretically (e.g consistency, asymptotical distribution) and by means of simulation experiments (e.g. comparisons of exact effectiveness of our method for different heavy tailed distributions). A specific problem is finding of an optimal threshold k, say, yielding a trade off in between of variance and bias of the Hill estimator. Simulation results by Embrechtset al. (1997) showed that the Hill estimator and its alternatives work well over large ranges of values for k in the case of Pareto distribution. However, Hill estimator is often giving wrong results for distributions different from the

Druh

D - Stať ve sborníku

CEP obor

BB - Aplikovaná statistika, operační výzkum

OECD FORD obor

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Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2012

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Proceedings of the 58th World Statistics Congress of the International Statistical Institute

ISBN

978-90-73592-33-9

ISSN

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e-ISSN

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Počet stran výsledku

9

Strana od-do

2985-2993

Název nakladatele

International Statistical Institute

Místo vydání

The Hague

Místo konání akce

Dublin

Datum konání akce

21. 8. 2011

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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