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

Eustasio del Barrio (Universidad de Valladolid)
Arnold Janssen (University of Düsseldorf)
Markus Pauly (University of Düsseldorf)

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.

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Pages: 1-10

Publication Date: December 3, 2013

DOI: 10.1214/ECP.v18-2772

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