Related papers: New Techniques for Empirical Process of Dependent …

Let $(U_n(t))_{t\in\R^d}$ be the empirical process associated to an $\R^d$-valued stationary process $(X_i)_{i\ge 0}$. We give general conditions, which only involve processes $(f(X_i))_{i\ge 0}$ for a restricted class of functions $f$,…

We provide a framework for empirical process theory of locally stationary processes using the functional dependence measure. Our results extend known results for stationary Markov chains and mixing sequences by another common possibility to…

Empirical processes for stationary, causal sequences are considered. We establish empirical central limit theorems for classes of indicators of left half lines, absolutely continuous functions and piecewise differentiable functions. Sample…

In this paper we survey some recent results on the central limit theorem and its weak invariance principle for stationary sequences. We also describe several maximal inequalities that are the main tool for obtaining the invariance…

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 provide an empirical process theory for locally stationary processes over nonsmooth function classes. An important novelty over other approaches is the use of the flexible functional dependence measure to quantify dependence. A…

In this paper, we prove maximal inequalities and study the functional central limit theorem for the partial sums of linear processes generated by dependent innovations. Due to the general weights, these processes can exhibit long-range…

This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields under natural and easily verifiable conditions. More precisely, we deal with random fields of the form $X_k =…

We establish a central limit theorem and an invariance principle for stationary random fields, with projective-type conditions. Our result is obtained via an m-dependent approximation method. As applications, we establish invariance…

We establish a multivariate empirical process central limit theorem for stationary $\R^d$-valued stochastic processes $(X_i)_{i\geq 1}$ under very weak conditions concerning the dependence structure of the process. As an application we can…

We investigate the convergence in distribution of sequential empirical processes of dependent data indexed by a class of functions F. Our technique is suitable for processes that satisfy a multiple mixing condition on a space of functions…

We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…

In this paper, a fourth moment bound for partial sums of functional of strongly ergodic Markov chain is established. This type of inequality plays an important role in the study of empirical process invariance principle. This one is…

We obtain necessary and sufficient conditions for the regular variation of the variance of partial sums of functionals of discrete and continuous-time stationary Markov processes with normal transition operators. We also construct a class…

We prove an invariance principle for non-stationary random processes and establish a rate of convergence under a new type of mixing condition. The dependence is exponentially decaying in the gap between the past and the future and is…

In this paper we study the asymptotic behavior of linear processes having as innovations mean zero, square integrable functions of stationary reversible Markov chains. In doing so we shall preserve the generality of coefficients assuming…

In this note, we prove a conditionally centered version of the quenched weak invariance principle under the Hannan condition, for stationary processes. In the course, we obtain a (new) construction of the fact that any stationary process…

Exponential inequalities are main tools in machine learning theory. To prove exponential inequalities for non i.i.d random variables allows to extend many learning techniques to these variables. Indeed, much work has been done both on…

Regularly varying stochastic processes are able to model extremal dependence between process values at locations in random fields. We investigate the empirical extremogram as an estimator of dependence in the extremes. We provide conditions…

In this article, we primarily propose a novel Bayesian characterization of stationary and nonstationary stochastic processes. In practice, this theory aims to distinguish between global stationarity and nonstationarity for both parametric…