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The $m(n)$ out of $k(n)$ bootstrap for partial sums of St. Petersburg type games

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	The $m(n)$ out of $k(n)$ bootstrap for partial sums of St. Petersburg type games
2.	Creator	Author's name, affiliation, country	Eustasio del Barrio; Universidad de Valladolid
2.	Creator	Author's name, affiliation, country	Arnold Janssen; University of Düsseldorf
2.	Creator	Author's name, affiliation, country	Markus Pauly; University of Düsseldorf
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Bootstrap, infinitely divisible distributions, L{\'e}vy process, $m(n)$ out of $k(n)$ resampling, stable and semi-stable laws, St. Petersburg game
3.	Subject	Subject classification	60E07, 62F40, 60F05.
4.	Description	Abstract	This paper illustrates that the bootstrap of a partial sum given by i.i.d. copies of a random variable $X_1$ has to be dealt with care in general. It turns out that in various cases a whole spectrum of different limit laws of the $m(n)$ out of $k(n)$ bootstrap can be obtained for different choices of $m(n)/k(n) -> 0$ whenever $X_1$ does not lie in the domain of attraction of a stable law. As a concrete example we study bootstrap limit laws for the cumulated gain sequence of repeated St. Petersburg games. It is shown that here a continuum of different semi-stable bootstrap limit laws occurs.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2013-12-03
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/2772
10.	Identifier	Digital Object Identifier	10.1214/ECP.v18-2772
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 18
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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