We study families of bounded real valued tied quantized chains. The chains are tied together by the assumption that there is a universal partition of the range, such that the distribution of the chains, conditioned on each interval of the partition is independent of the chain. We define a new class of cross estimators for the cut-points separating these intervals and prove their asymptotic consistency. We apply our results to model the sonority time evolution of different languages using a linguistic corpus with 1667 sentences from eight different languages. We show that a model with four universal cut-points is in good agreement with the data. The new notion of family of tied quantized chains should be relevant for modeling other situations in which different stochastic agents express themselves using the same type of interface.
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