Affiliation:
1. Department of Statistics, University of Campinas, Campinas 13083-859, São Paulo, Brazil
Abstract
This paper extends the concept of metrics based on the Bayesian information criterion (BIC), to achieve strongly consistent estimation of partition Markov models (PMMs). We introduce a set of metrics drawn from the family of model selection criteria known as efficient determination criteria (EDC). This generalization extends the range of options available in BIC for penalizing the number of model parameters. We formally specify the relationship that determines how EDC works when selecting a model based on a threshold associated with the metric. Furthermore, we improve the penalty options within EDC, identifying the penalty ln(ln(n)) as a viable choice that maintains the strongly consistent estimation of a PMM. To demonstrate the utility of these new metrics, we apply them to the modeling of three DNA sequences of dengue virus type 3, endemic in Brazil in 2023.
Funder
CAPES with fellowships from the Master Graduate Program in Statistics—University of Campinas
Reference11 articles.
1. On determination of the order of a Markov chain;Zhao;Stat. Inference Stoch. Process.,2001
2. García Jesús, E., and González-López, V.A. (2017). Consistent Estimation of Partition Markov Models. Entropy, 19.
3. García, J.E., González-López, V.A., Tasca, G.H., and Yaginuma, K.Y. (2022). An Efficient Coding Technique for Stochastic Processes. Entropy, 24.
4. Pereira, D.F.S. (2021). Critério de Determinação Eficiente Para Estimação de Cadeias de Markov de Partição Mínima. [Master’s Thesis, University of Brasilia]. Available online: http://repositorio2.unb.br/jspui/handle/10482/42891.
5. Optimal penalty term for EDC Markov chain order estimator;Dorea;Ann. de l’ISUP,2008