Estimating the index of a stable law via the pot-method

Consider an i.i.d. sample X1,...,Xn of random variables which are equal in distribution to Y, where Y follows a symmetric stable law with index [beta], 0 < [beta] < 2. Based on the point process of exceedances, we define an explicit two-step-estimator of [beta] that is asymptotically efficient. Adding a scale parameter as a nuisance parameter, the Hill estimator turns out to be asymptotically efficient. Simulations exemplify the results.

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Year of publication:	1999
Authors:	Marohn, Frank
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 41.1999, 4, p. 413-423
Publisher:	Elsevier
Keywords:	Stable distribution Point process of exceedances Peaks over threshold Generalized Pareto distribution Hill estimator LAN Central sequence Asymptotic efficiency Finite sample size properties

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://ebvufind01.dmz1.zbw.eu/10005224087