A sequential empirical CLT for multiple mixing processes with application to $\mathcal{B}$-geometrically ergodic Markov chains
Olivier Durieu (Université de Tours)
Marco Tusche (Ruhr-Universität Bochum & Université de Tours)
Abstract
We investigate the convergence in distribution of sequential empirical processes of dependent data indexed by a class of functions F. Our technique is suitable for processes that satisfy a multiple mixing condition on a space of functions which differs from the class F. This situation occurs in the case of data arising from dynamical systems or Markov chains, for which the Perron-Frobenius or Markov operator, respectively, has a spectral gap on a restricted space. We provide applications to iterative Lipschitz models that contract on average.
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Pages: 1-26
Publication Date: September 20, 2014
DOI: 10.1214/EJP.v19-3216
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