English

Some limits to nonparametric estimation for ergodic processes

Information Theory 2011-02-17 v1 math.IT

Abstract

A new negative result for nonparametric distribution estimation of binary ergodic processes is shown. The problem of estimation of distribution with any degree of accuracy is studied. Then it is shown that for any countable class of estimators there is a zero-entropy binary ergodic process that is inconsistent with the class of estimators. Our result is different from other negative results for universal forecasting scheme of ergodic processes. We also introduce a related result by B. Weiss.

Cite

@article{arxiv.1102.3241,
  title  = {Some limits to nonparametric estimation for ergodic processes},
  author = {Hayato Takahashi},
  journal= {arXiv preprint arXiv:1102.3241},
  year   = {2011}
}

Comments

submitted to ISIT2011

R2 v1 2026-06-21T17:27:01.762Z