An empirical central limit theorem in L¹ for stationary sequences

2008/12/15 by Dede, Sophie
#60F17 #60G10 #62G30 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.0812.2839

Abstract

In this paper, we derive asymptotic results for L¹-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 L¹. The conditions obtained are expressed in terms of projective-type conditions. The main tools are martingale approximations.

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