Details

Autor(en) / Beteiligte

• Maumy, Myriam
• Varron, Davit

Titel

Non standard functional limit laws for the increments of the compound empirical distribution function

Ist Teil von

• Electronic journal of statistics, 2010-01, Vol.4 (none), p.1324-1344

Ort / Verlag

Shaker Heights, OH : Institute of Mathematical Statistics

Erscheinungsjahr

2010

Quelle

EZB Electronic Journals Library

Beschreibungen/Notizen

• Let (Y i , Z i) i≥1 be a sequence of independent, identically distributed (i.i.d.) random vectors taking values in R k × R d , for some integers k and d. Given z ∈ R d , we provide a nonstandard functional limit law for the sequence of functional increments of the compound empirical process, namely ∆n,c(hn, z, ·) := 1 nhn n i=1 1 [0,·) Z i − z hn 1/d Y i. Provided that nhn ∼ c log n as n → ∞, we obtain, under some natural conditions on the conditional exponential moments of Y | Z = z, that ∆n,c(hn, z, ·) Γ almost surely, where denotes the clustering process under the sup norm on [0, 1) d. Here, Γ is a compact set that is related to the large deviations of certain compound Poisson processes.