New Techniques for Empirical Process of Dependent Data

Details New Techniques for Empirical Process of Dependent Data New Techniques for Empirical Process of Dependent Data

2008-06-18

arxiv.org/abs/0806.2941v2

Mathematics

Probability

Scientific paper

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.

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