Segmentação de sequências em cadeias de Markov usando máxima verossimilhança penalizada - Rodrigues, Franklin Diego de Lima (2023)
The sequence segmentation problem aims to partition a sequence or a set of them into a finite number of distinct segments as homogeneous as possible. In this paper, we consider the problem of segmenting a set of random sequences, with values in a finite alphabet E, into a finite number of independent blocks. Under the assumption that the data follow a Markov chain, the problem consists in estimating the number and position of the change points in the sequence. For this, we propose the using of the penalized maximum likelihood criterion to infer, simultaneously, the number and position of the change points. The main result of our work is the demonstration of the theorem that guarantees the strong consistency of the set of change points estimators for a sufficiently large number of samples.