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The starting point of this article is the question "How to retrievefingerprints of rhythm in written texts?" We address this problem in the caseof Brazilian and European Portuguese. These two dialects of Modern Portugueseshare the same lexicon and most of the sentences they produce are superficiallyidentical. Yet they are conjectured, on linguistic grounds, to implementdifferent rhythms. We show that this linguistic question can be formulated as aproblem of model selection in the class of variable length Markov chains. Tocarry on this approach, we compare texts from European and BrazilianPortuguese. These texts are previously encoded according to some basic rhythmicfeatures of the sentences which can be automatically retrieved. This is anentirely new approach from the linguistic point of view. Our statisticalcontribution is the introduction of the smallest maximizer criterion which is aconstant free procedure for model selection. As a by-product, this provides asolution for the problem of optimal choice of the penalty constant when usingthe BIC to select a variable length Markov chain. Besides proving theconsistency of the smallest maximizer criterion when the sample size diverges,we also make a simulation study comparing our approach with both the standardBIC selection and the Peres-Shields order estimation. Applied to the linguisticsample constituted for our case study, the smallest maximizer criterion assignsdifferent context-tree models to the two dialects of Portuguese. The featuresof the selected models are compatible with current conjectures discussed in thelinguistic literature.

Context tree selection and linguistic rhythm retrieval from written texts