| Título: | The $m(n)$ out of $k(n)$ bootstrap for partial sums of St. Petersburg type games |
| Autores: |
del Barrio, Eustasio; Universidad de Valladolid Janssen, Arnold; University of Düsseldorf Pauly, Markus; University of Düsseldorf |
| Fecha: | 2013-01-03 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
Bootstrap, infinitely divisible distributions, L{\'e}vy process, $m(n)$ out of $k(n)$ resampling, stable and semi-stable laws, St. Petersburg game 60E07, 62F40, 60F05. |
| Descripción: | 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. |
| Idioma: | Inglés |
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