Tópicos em seleção de modelos markovianos / Topics in selection of Markov models


IBICT - Instituto Brasileiro de Informação em Ciência e Tecnologia




This work related two statistical problems involving the selection of a Markovian model of finite order. Firstly, we propose a procedure to choose a context tree from independent samples, with more than half of them being realizations of the same finite memory Markovian processes with finite alphabet with law P. Our model selection strategy is based on estimating relative entropies to select a subset of samples that are realizations of the same law. We define the asymptotic breakdown point for a model selection procedure, and show the asymptotic breakdown point for our procedure. Moreover, we study the robust procedure by simulations and it is applied to linguistic data. The aim of other problem is to develop a consistent methodology for obtain the finner partitions of the coordinates of an multivariate Markovian stationary process such that their elements are conditionally independents. The proposed method is establishment by Bayesian information criterion (BIC). However, when the number of the coordinates of process increases, the computing of criterion BIC becomes excessive. In this case, we propose an algorithm more efficient and the its consistency is demonstrated. It is tested by simulations and applied to linguistic data.


markov processos de estatistica robusta comprimento minimo de descrição (teoria da informação) compressão de dados (computação) markov processes robust statisitica iminimum description lengh (information theory) data compression (computer science)

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