Nonparametric Estimation and On-Line Prediction for General Stationary Ergodic Sources

Details Nonparametric Estimation and On-Line Prediction for General Stationary Ergodic Sources Nonparametric Estimation and On-Line Prediction for General Stationary Ergodic Sources

2010-02-24

arxiv.org/abs/1002.4453v3

Computer Science

Information Theory

Scientific paper

We proposed a learning algorithm for nonparametric estimation and on-line prediction for general stationary ergodic sources. We prepare histograms each of which estimates the probability as a finite distribution, and mixture them with weights to construct an estimator. The whole analysis is based on measure theory. The estimator works whether the source is discrete or continuous. If it is stationary ergodic, then the measure theoretically given Kullback-Leibler information divided by the sequence length $n$ converges to zero as $n$ goes to infinity. In particular, for continuous sources, the method does not require existence of a probability density function.

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