Selection from a stable box

dc.creatorAue, Alexander
dc.creatorBerkes, István
dc.creatorHorváth, Lajos
dc.date2008-03-06
dc.date.accessioned2026-07-07T12:17:27Z
dc.date.available2026-07-07T12:17:27Z
dc.descriptionLet $\{X_j\}$ 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.descriptionPublished 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.identifierhttps://arxiv.org/abs/0803.0868
dc.identifierhttp://arxiv.org/abs/0803.0868
dc.identifierBernoulli 2008, Vol. 14, No. 1, 125-139
dc.identifierdoi:10.3150/07-BEJ6014
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/212085
dc.subjectStatistics Theory
dc.titleSelection from a stable box
dc.typetext

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