Related papers: A weak convergence result for sequential empirical…

We offer an umbrella type result which extends weak convergence of the classical empirical process on the line to that of more general processes indexed by functions of bounded variation. This extension is not contingent on the type of…

We study the sequential empirical process indexed by general function classes and its smoothed set-indexed analogue. Sufficient conditions for asymptotic equicontinuity are provided for nonstationary arrays of time series. This yields…

Weak convergence of the empirical copula process indexed by a class of functions is established. Two scenarios are considered in which either some smoothness of these functions or smoothness of the underlying copula function is required. A…

This article investigates weak convergence of the sequential $d$-dimensional empirical process under strong mixing. Weak convergence is established for mixing rates $\alpha_n = O(n^{-a})$, where $a>1$, which slightly improves upon existing…

In this paper, we study the weak convergence of the integrated periodogram indexed by classes of functions for linear processes with symmetric $\alpha$-stable innovations. Under suitable summability conditions on the series of the Fourier…

In the past decades, weak convergence theory for stochastic processes has become a standard tool for analyzing the asymptotic properties of various statistics. Routinely, weak convergence is considered in the space of bounded functions…

The empirical copula has proved to be useful in the construction and understanding of many statistical procedures related to dependence within random vectors. The empirical beta copula is a smoothed version of the empirical copula that…

The empirical copula process plays a central role in the asymptotic analysis of many statistical procedures which are based on copulas or ranks. Among other applications, results regarding its weak convergence can be used to develop…

We investigate a particular form of weak convergence of the local empirical process.

We study weak convergence of empirical processes of dependent data $(X_i)_{i\geq0}$, indexed by classes of functions. Our results are especially suitable for data arising from dynamical systems and Markov chains, where the central limit…

We consider statistical learning question for $\psi$-weakly dependent processes, that unifies a large class of weak dependence conditions such as mixing, association,$\cdots$ The consistency of the empirical risk minimization algorithm is…

(English) This monograph aims at presenting the core weak convergence theory for sequences of random vectors with values in $\mathbb{R}^k$. In some places, a more general formulation in metric spaces is provided. It lays out the necessary…

This work provides some general theorems about unconditional and conditional weak convergence of empirical processes in the case of Poisson sampling designs. The theorems presented in this work are stronger than previously published…

For a strictly stationary sequence of random variables we derive functional convergence of the joint partial sum and partial maxima process under joint regular variation with index $\alpha \in (0,2)$ and weak dependence conditions. The…

In this paper, weak convergences of marked empirical processes in $L^2(\mathbb{R},\nu)$ and their applications to statistical goodness-of-fit tests are provided, where $L^2(\mathbb{R},\nu)$ is the set of equivalence classes of the square…

A time-varying empirical spectral process indexed by classes of functions is defined for locally stationary time series. We derive weak convergence in a function space, and prove a maximal exponential inequality and a…

We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also…

Let $(X_j)_{j\geq1}$ be a multivariate long-range dependent Gaussian process. We study the asymptotic behavior of the corresponding sequential empirical process indexed by a class of functions. If some entropy condition is satisfied we have…

While effective concentration inequalities for suprema of empirical processes exist under boundedness or strict tail assumptions, no comparable results have been available under considerably weaker assumptions. In this paper, we derive…

We introduce a maximal inequality for a local empirical process under strongly mixing data. Local empirical processes are defined as the (local) averages $\frac{1}{nh}\sum_{i=1}^n \mathbf{1}\{x - h \leq X_i \leq x+h\}f(Z_i)$, where $f$…