Empirical Quantile CLTs for Time Dependent Data
Abstract
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 - 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.
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