An empirical central limit theorem in L^1 for stationary sequences

Sophie Dede

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arXiv · 0812.2839

An empirical central limit theorem in L^1 for stationary sequences

Sophie Dede

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Abstract

In this paper, we derive asymptotic results for L^1-Wasserstein distance between the distribution function and the corresponding empirical distribution function of a stationary sequence. Next, we give some applications to dynamical systems and causal linear processes. To prove our main result, we give a Central Limit Theorem for ergodic stationary sequences of random variables with values in L^1. The conditions obtained are expressed in terms of projective-type conditions. The main tools are martingale approximations.

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BibTeX RIS

Sophie Dede. 2008-12-15. An empirical central limit theorem in L^1 for stationary sequences. https://arxiv.org/abs/0812.2839

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