Universal Linear Least-Squares Prediction in the Presence of Noise

Authors:
Georg C. Zeitler;Andrew C. Singer
Affiliations:
University of Illinois, Urbana-Champaign, Department of Electrical and Computer Engineering, Urbana, IL 61801;University of Illinois, Urbana-Champaign, Department of Electrical and Computer Engineering, Urbana, IL 61801
Venue:
SSP '07 Proceedings of the 2007 IEEE/SP 14th Workshop on Statistical Signal Processing
Year:
2007

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Abstract

Universal linear least squares prediction of real-valued bounded individual sequences in the presence of additive bounded noise is considered. It is shown that there is a sequential predictor observing noisy samples of the sequence to be predicted only, whose loss in terms of the noise-free sequence is asymptotically as small as that of the best batch predictor out of the class of all linear predictors with knowledge of the entire noisy sequence in advance.