Redundancy of the Context-tree Weighting Method on Renewal and Markov Renewal Processes
IEEE Transactions on Information Theory
The Context Tree Weighting method is almost adaptive on the classes of renewal and Markov renewal processes : it achieves the minimax pointwise redundancy, studied by Imre Csisz\'ar and Paul C. Shields, up to logarithmic factor.
On a theoretical level, this result may be regarded as adaptive estimation in a non parametric setting.
On a more practical level, this result furnishes a first example of a universal coder efficient on intermediate complexity classes.