Nonparametric statistical inference for the context tree of a stationary ergodic process

Autor(es)

Gallo, Sandro ^[1] ; Leonardi, Florencia ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed Sao Carlos, Dept Stat, BR-13560 Sao Carlos, SP - Brazil

^[2] Univ Sao Paulo, Inst Math & Stat, BR-05508 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: ELECTRONIC JOURNAL OF STATISTICS; v. 9, n. 2, p. 2076-2098, 2015.
• Citações Web of Science: 0

Resumo

We consider the problem of estimating the context tree of a stationary ergodic process with finite alphabet without imposing additional conditions on the process. As a starting point we introduce a Hamming metric in the space of irreducible context trees and we use the properties of the weak topology in the space of ergodic stationary processes to prove that if the Hamming metric is unbounded, there exist no consistent estimators for the context tree. Even in the bounded case we show that there exist no two-sided confidence bounds. However we prove that one-sided inference is possible in this general setting and we construct a consistent estimator that is a lower bound for the context tree of the process with an explicit formula for the coverage probability. We develop an efficient algorithm to compute the lower bound and we apply the method to test a linguistic hypothesis about the context tree of codified written texts in European Portuguese. (AU)

• Processo FAPESP: 13/07699-0 - Centro de Pesquisa, Inovação e Difusão em Neuromatemática - NeuroMat
• Beneficiário: Jefferson Antonio Galves
• Linha de fomento: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs
• Processo FAPESP: 15/09094-3 - Cadeias estocásticas de longo alcance
• Beneficiário: Alexsandro Giacomo Grimbert Gallo
• Linha de fomento: Auxílio à Pesquisa - Regular