Title :
Some limits to nonparametric estimation for ergodic processes
Author :
Takahashi, Hayato
Author_Institution :
Inst. of Stat. Math., Tokyo, Japan
fDate :
July 31 2011-Aug. 5 2011
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.
Keywords :
entropy; nonparametric statistics; statistical distributions; binary ergodic processes; entropy; nonparametric distribution estimation; universal forecasting scheme; Accuracy; Convergence; Entropy; Estimation; Information theory; Nickel; System-on-a-chip; computable function; cutting and stacking; ergodic process; nonparametric estimation;
Conference_Titel :
Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on
Conference_Location :
St. Petersburg
Print_ISBN :
978-1-4577-0596-0
Electronic_ISBN :
2157-8095
DOI :
10.1109/ISIT.2011.6034015
