Some upper bounds for the rate of convergence of penalized likelihood context tree estimators

DOI10.1214/09-BJPS033zbMath1192.62193arXivmath/0701810MaRDI QIDQ985992

Florencia Leonardi

Publication date: 9 August 2010

Published in: Brazilian Journal of Probability and Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701810

zbMATH Keywords

rate of convergenceBayesian information criterionpenalized maximum likelihood estimationcontext tree

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Non-Markovian processes: estimation (62M09) Inference from stochastic processes (62M99)

Related Items (2)

Divergence rates of Markov order estimators and their application to statistical estimation of stationary ergodic processes ⋮ Context tree selection: a unifying view

Cites Work

• Markov approximation and consistent estimation of unbounded probabilistic suffix trees
• Processes with long memory: Regenerative construction and perfect simulation
• Variable length Markov chains
• Exponential bounds for the probability of wrong determination of the order of a Markov chain by using the EDC criterion
• Exponential inequalities for empirical unbounded context trees
• Context tree estimation for not necessarily finite memory processes, via BIC and MDL
• Consistency of the Unlimited BIC Context Tree Estimator
• A universal data compression system
• The context-tree weighting method: extensions
• Estimation of General Stationary Processes by Variable Length Markov Chains
• The context-tree weighting method: basic properties
• The optimal error exponent for Markov order estimation
• Exponential inequalities for VLMC empirical trees

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