Title :
Computational Limits to Nonparametric Estimation for Ergodic Processes
Author :
Takahashi, Hayato
Author_Institution :
Inst. of Stat. Math., Tokyo, Japan
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.
Keywords :
entropy; estimation theory; forecasting theory; computational limit; estimators countable class; nonparametric distribution estimation; universal forecasting scheme; zero-entropy binary ergodic process; Accuracy; Convergence; Entropy; Estimation; Stacking; System-on-a-chip; Trajectory; Computable function; cutting and stacking; ergodic process; nonparametric estimation;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2011.2165791
