2011/11/19 by James Kuelbs, Kuelbs, James, Joel Zinn +1 · 1 citation
Mathematics · #60F05 (Primary) 60F17 #62E20 (Secondary) #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST) #math.PR #math.ST #msc:60F05 #msc:60F17 #msc:62E20 #stat.TH
paper · pdf · doi:10.48550/arxiv.1111.4591
52 pages
arxiv created 2011/11/19 · arxiv updated 2011/11/22
We establish empirical quantile process CLTs based on n independent copies of a stochastic process \Xt: t ∈ E\ that are uniform in t ∈ E and quantile levels α∈ I, where I is a closed sub-interval of (0,1). Typically E=[0,T], or a finite product of such intervals. Also included are CLT's for the empirical process based on \IXt ≤ y - \rm Pr(Xt ≤ y): t ∈ E, y ∈ R \ that are uniform in t ∈ E, y ∈ R. The process \Xt: t ∈ E\ may be chosen from a broad collection of Gaussian processes, compound Poisson processes, stationary independent increment stable processes, and martingales.