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Journal Articles Stochastic Processes and their Applications Year : 2009

New Techniques for Empirical Process of Dependent Data

Abstract

We present a new technique for proving empirical process invariance principle for stationary processes $(X_n)_{n\geq 0}$. The main novelty of our approach lies in the fact that we only require the central limit theorem and a moment bound for a restricted class of functions $(f(X_n))_{n\geq 0}$, not containing the indicator functions. Our approach can be applied to Markov chains and dynamical systems, using spectral properties of the transfer operator. Our proof consists of a novel application of chaining techniques.

Dates and versions

hal-00291501 , version 1 (27-06-2008)

Identifiers

Cite

Herold Dehling, Olivier Durieu, Dalibor Volný. New Techniques for Empirical Process of Dependent Data. Stochastic Processes and their Applications, 2009, 119, pp.3699-3718. ⟨10.1016/j.spa.2009.07.003⟩. ⟨hal-00291501⟩
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