Some limits to nonparametric estimation for ergodic processes

2011/02/16 by Hayato Takahashi, Takahashi, Hayato
Computer Science · Economics, Econometrics and Finance · Mathematics · #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #Information Theory (cs.IT) #Mathematical Dynamics and Fractals #Stochastic processes and financial applications #cs.IT #math.IT

paper · pdf · doi:10.48550/arxiv.1102.3241

submitted to ISIT2011

arxiv created 2011/02/16 · openalex publication_date 2011/02/16 · arxiv updated 2011/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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