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 />
Citation
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
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