### Abstract

We consider the problem of sequential linear prediction of real-valued sequences under the square-error loss function. For this problem, a prediction algorithm has been demonstrated whose accumulated squared prediction error, for every bounded sequenee, is asymptotically as small as the best fixed linear predictor for that sequence, taken from the class of all linear predictors of a given order p. The redundancy, or excess prediction error above that of the best predictor for that sequence, is upper bounded by A^{2}p ln(n)/n, where n is the data length and the sequence is assumed to be bounded by some A. In this paper, we show that this predictor is optimal in a min-max sense, by deriving a corresponding lower bound, such that no sequential predictor can ever do better than a redundancy of A^{2}p ln(n)/n.

Original language | English (US) |
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Number of pages | 1 |

Journal | IEEE International Symposium on Information Theory - Proceedings |

State | Published - Sep 12 2002 |

Event | 2002 IEEE International Symposium on Information Theory - Lausanne, Switzerland Duration: Jun 30 2002 → Jul 5 2002 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Information Systems
- Modeling and Simulation
- Applied Mathematics

### Cite this

**A lower bound on the performance of sequential prediction.** / Kozat, Suleyman S.; Singer, Andrew Carl.

Research output: Contribution to journal › Conference article

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TY - JOUR

T1 - A lower bound on the performance of sequential prediction

AU - Kozat, Suleyman S.

AU - Singer, Andrew Carl

PY - 2002/9/12

Y1 - 2002/9/12

N2 - We consider the problem of sequential linear prediction of real-valued sequences under the square-error loss function. For this problem, a prediction algorithm has been demonstrated whose accumulated squared prediction error, for every bounded sequenee, is asymptotically as small as the best fixed linear predictor for that sequence, taken from the class of all linear predictors of a given order p. The redundancy, or excess prediction error above that of the best predictor for that sequence, is upper bounded by A2p ln(n)/n, where n is the data length and the sequence is assumed to be bounded by some A. In this paper, we show that this predictor is optimal in a min-max sense, by deriving a corresponding lower bound, such that no sequential predictor can ever do better than a redundancy of A2p ln(n)/n.

AB - We consider the problem of sequential linear prediction of real-valued sequences under the square-error loss function. For this problem, a prediction algorithm has been demonstrated whose accumulated squared prediction error, for every bounded sequenee, is asymptotically as small as the best fixed linear predictor for that sequence, taken from the class of all linear predictors of a given order p. The redundancy, or excess prediction error above that of the best predictor for that sequence, is upper bounded by A2p ln(n)/n, where n is the data length and the sequence is assumed to be bounded by some A. In this paper, we show that this predictor is optimal in a min-max sense, by deriving a corresponding lower bound, such that no sequential predictor can ever do better than a redundancy of A2p ln(n)/n.

UR - http://www.scopus.com/inward/record.url?scp=0036350890&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036350890&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0036350890

JO - IEEE International Symposium on Information Theory - Proceedings

JF - IEEE International Symposium on Information Theory - Proceedings

SN - 2157-8095

ER -