Some limits to nonparametric estimation for ergodic processes

Details Some limits to nonparametric estimation for ergodic processes Some limits to nonparametric estimation for ergodic processes

2011-02-16

arxiv.org/abs/1102.3241v1

Computer Science

Information Theory

submitted to ISIT2011

Scientific paper

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.

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