Selection from a stable box
| dc.creator | Aue, Alexander | |
| dc.creator | Berkes, István | |
| dc.creator | Horváth, Lajos | |
| dc.date | 2008-03-06 | |
| dc.date.accessioned | 2026-07-07T12:17:27Z | |
| dc.date.available | 2026-07-07T12:17:27Z | |
| dc.description | Let $\{X_j\}$ be independent, identically distributed random variables. It is well known that the functional CUSUM statistic and its randomly permuted version both converge weakly to a Brownian bridge if second moments exist. Surprisingly, an infinite-variance counterpart does not hold true. In the present paper, we let $\{X_j\}$ be in the domain of attraction of a strictly $α$-stable law, $α\in(0,2)$. While the functional CUSUM statistics itself converges to an $α$-stable bridge and so does the permuted version, provided both the $\{X_j\}$ and the permutation are random, the situation turns out to be more delicate if a realization of the $\{X_j\}$ is fixed and randomness is restricted to the permutation. Here, the conditional distribution function of the permuted CUSUM statistics converges in probability to a random and nondegenerate limit. | |
| dc.description | Published in at http://dx.doi.org/10.3150/07-BEJ6014 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm) | |
| dc.identifier | https://arxiv.org/abs/0803.0868 | |
| dc.identifier | http://arxiv.org/abs/0803.0868 | |
| dc.identifier | Bernoulli 2008, Vol. 14, No. 1, 125-139 | |
| dc.identifier | doi:10.3150/07-BEJ6014 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/212085 | |
| dc.subject | Statistics Theory | |
| dc.title | Selection from a stable box | |
| dc.type | text |