On optimal sequential prediction for general processes
Public Deposited- Creator
- Nobel, Andrew
- Abstract
- In the stochastic sequential prediction problem, the elements of a random process X 1 , X 2 , ... 2 R are successively revealed to a forecaster. At each time t the forecaster makes a prediction F t of X t based only on X 1 , ..., X t 1 , when X t is revealed, the forecaster incurs a loss `(F t , X t ). This paper considers several aspects of the sequential prediction problem for unbounded, non-stationary processes under p-th power loss , 1 < p < 1. In the first part of the paper it is shown that Bayes prediction schemes are Cesaro optimal under general conditions, that Cesaro optimal prediction schemes are unique in a natural sense, and that Cesaro optimality is equivalent to a form of weak calibration. Extensions of the existence and uniqueness results to generalized prediction, and prediction from observations with additive noise, are established.
- Date of publication
- 2003
- DOI
- Identifier
- Onescience ID: 9e22744a9f831022b728c9d14f064f3aa0c56cf6
- https://dx.doi.org/10.1109/TIT.2002.806141
- Resource type
- Article
- Rights statement
- In Copyright
- Journal title
- IEEE Transactions on Information Theory
- Journal volume
- 49
- Journal issue
- 1
- Page start
- 83
- Page end
- 98
- Language
- English
- Version
- Preprint
- ISSN
- 1557-9654
- 0018-9448
Relations
- Parents:
This work has no parents.
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