Weak Convergence of Stationary Empirical Processes

An elementary proof of the weak convergence of empirical processes

This paper develops a simple technique for proving the weak convergence of a stochastic process Z̄n(g) := ∫ g dZn, indexed by functions g in some class G. The main novelty is a decoupling argument that allows to derive asymptotic equicontinuity of the process {Z̄n(g), g ∈ G} from that of the basic process {Zn(t), t ∈ R}, with Zn(t) = Z̄n(ft) and ft(x) = 1(−∞,t](x). The method leads to novel result...

@bullet , @bullet Weak Convergence of Multidimensional Empirical Processes for Stationary ¢-mixing Processes

Empirical Processes of Stationary Sequences

The paper considers empirical distribution functions of stationary causal processes. Weak convergence of normalized empirical distribution functions to Gaussian processes is established and sample path properties are discussed. The Chibisov-O’Reilly Theorem is generalized to dependent random variables. The proposed dependence structure is related to the sensitivity measure, a quantity appearing...

I I . I I I I Limiting Behavior of Regular Functionals of Empirical Distributions for Stationary

SUMMARY. For a stationary *-mixing stochastic process, the law of iterated logarithm, asymptotic normality and weak convergence to Brownian motion processes

The Tail Empirical Process for Stationary Sequences

Diagnostic plots are an important part of extreme value statistics. This paper provides a theoretical basis for such plots by proving weak convergence of the tail empirical process for a large class of stationary processes. The conditions needed for convergence are (i) restrictions on the long-range dependence (mixing), (ii) moment restrictions on the amount of clustering of extremes, and (iii)...