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2013 The $m(n)$ out of $k(n)$ bootstrap for partial sums of St. Petersburg type games
Eustasio del Barrio, Arnold Janssen, Markus Pauly
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Electron. Commun. Probab. 18: 1-10 (2013). DOI: 10.1214/ECP.v18-2772

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. <br />

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Eustasio del Barrio. Arnold Janssen. Markus Pauly. "The $m(n)$ out of $k(n)$ bootstrap for partial sums of St. Petersburg type games." Electron. Commun. Probab. 18 1 - 10, 2013. https://doi.org/10.1214/ECP.v18-2772

Information

Accepted: 3 December 2013; Published: 2013
First available in Project Euclid: 7 June 2016

zbMATH: 1339.60016
MathSciNet: MR3145047
Digital Object Identifier: 10.1214/ECP.v18-2772

Subjects:
Primary: 60E07
Secondary: 60F05, 62F40

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