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Concentration of empirical entropy and transfer entropy for non-regular chains with unbounded memory

  • José O. Santana
  • Ricardo F. Ferreira
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Abstract

We study plug-in estimators of the entropy rate and the transfer entropy rate for stationary finite-alphabet chains with unbounded memory. Under a coalescent coupling-from-the-past assumption, we establish non-asymptotic concentration inequalities around the expectations of the estimators. Under additional uniform non-nullness and exponential beta-mixing assumptions, we control the corresponding biases and obtain concentration around the entropy and transfer entropy rates, together with almost-sure consistency. The results apply to chains governed by g-functions that need not be globally continuous.

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Cite

BibTeXRIS
BibTeX
@misc{santana2026concentration,
  title = {{Concentration of empirical entropy and transfer entropy for non-regular chains with unbounded memory}},
  author = {José O. Santana and Ricardo F. Ferreira},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.32713},
  eprint = {2609.32713},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.32713},
}
RIS
TY  - UNPB
TI  - Concentration of empirical entropy and transfer entropy for non-regular chains with unbounded memory
AU  - José O. Santana
AU  - Ricardo F. Ferreira
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.32713
UR  - https://arxiv.org/abs/2609.32713
AB  - We study plug-in estimators of the entropy rate and the transfer entropy rate for stationary finite-alphabet chains with unbounded memory. Under a coalescent coupling-from-the-past assumption, we establish non-asymptotic concentration inequalities around the expectations of the estimators. Under additional uniform non-nullness and exponential beta-mixing assumptions, we control the corresponding biases and obtain concentration around the entropy and transfer entropy rates, together with almost-sure consistency. The results apply to chains governed by g-functions that need not be globally continuous.
ER  -