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Asymptotic Normality of Hill Estimator for Truncated Data

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1.	Title	Title of document	Asymptotic Normality of Hill Estimator for Truncated Data
2.	Creator	Author's name, affiliation, country	Arijit Chakrabarty; Indian Statistical Institute; India
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	heavy tails, truncation, second order regular variation, Hill estimator, asymptotic normality
3.	Subject	Subject classification	62G32
4.	Description	Abstract	The problem of estimating the tail index from truncated data is addressed in [2]. In that paper, a sample based (and hence random) choice of k is suggested, and it is shown that the choice leads to a consistent estimator of the inverse of the tail index. In this paper, the second order behavior of the Hill estimator with that choice of k is studied, under some additional assumptions. In the untruncated situation, asymptotic normality of the Hill estimator is well known for distributions whose tail belongs to the Hall class, see [11]. Motivated by this, we show the same in the truncated case for that class.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Research partially supported by the NSF grant ``Graduate and Postdoctoral Training in Probability and its Applications'' at Cornell University, the Centenary Post Doctoral Fellowship at the Indian Institute of Science and a fellowship from the National Bo
7.	Date	(YYYY-MM-DD)	2011-10-31
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/935
10.	Identifier	Digital Object Identifier	10.1214/EJP.v16-935
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 16
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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