New techniques for empirical processes of dependent data

Herold Dehling, Olivier Durieu and Dalibor Volny

Stochastic Processes and their Applications, 2009, vol. 119, issue 10, 3699-3718

Abstract: We present a new technique for proving the empirical process invariance principle for stationary processes (Xn)n>=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(Xn))n>=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.

Keywords: Empirical; process; Invariance; principle; Markov; chain; Dynamical; system; Chaining (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (9)

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