New Techniques for Empirical Process of Dependent Data

2008/06/18 by Herold Dehling, Dehling, Herold, Olivier Durieu +3
Mathematics · Physics and Astronomy · #60F17 #60G10 #62G30 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Quantum chaos and dynamical systems #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.0806.2941

openalex publication_date 2008/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a new technique for proving empirical process invariance principle for stationary processes (X_n)_{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(X_n))_{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.

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