A limited in bandwidth uniformity for the functional limit law of the increments of the empirical process

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dc.creatorVarron, Davit
dc.date2008-02-19
dc.date2008-11-13
dc.date.accessioned2026-07-07T10:17:34Z
dc.date.available2026-07-07T10:17:34Z
dc.descriptionConsider the following local empirical process indexed by $K\in \mathcal{G}$, for fixed $h>0$ and $z\in \mathbb{R}^d$: $$G_n(K,h,z):=\sum_{i=1}^n K \Bigl(\frac{Z_i-z}{h^{1/d}}\Big) - \mathbbE \Bigl(K \Bigl(\frac{Z_i-z}{h^{1/d}}\Big)\Big),$$ where the $Z_i$ are i.i.d. on $\mathbb{R}^d$. We provide an extension of a result of Mason (2004). Namely, under mild conditions on $\mathcal{G}$ and on the law of $Z_1$, we establish a uniform functional limit law for the collections of processes $\bigl\{G_n(\cdot,h_n,z), z\in H, h\in [h_n,\mathfrak{h}_n]\big\}$, where $H\subset \mathbb{R}^d$ is a compact set with nonempty interior and where $h_n$ and $\mathfrak{h}_n$ satisfy the Csörgő-Révész-Stute conditions.
dc.descriptionPublished in at http://dx.doi.org/10.1214/08-EJS193 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0802.2636
dc.identifierhttp://arxiv.org/abs/0802.2636
dc.identifierElectronic Journal of Statistics 2008, Vol. 2, 1043-1064
dc.identifierdoi:10.1214/08-EJS193
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173898
dc.subjectStatistics Theory
dc.subject60F15, 60F17 (Primary) 62G07 (Secondary)
dc.titleA limited in bandwidth uniformity for the functional limit law of the increments of the empirical process
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