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Exponential inequalities for VLMC empirical trees

Antonio GalvesVéronique Maume-DeschampsBernard Schmitt — 2008

ESAIM: Probability and Statistics

A seminal paper by Rissanen, published in 1983, introduced the class of Variable Length Markov Chains and the algorithm Context which estimates the probabilistic tree generating the chain. Even if the subject was recently considered in several papers, the central question of the rate of convergence of the algorithm remained open. This is the question we address here. We provide an exponential upper bound for the probability of incorrect estimation of the probabilistic tree, as a function...

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