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      • Department of Electrical and Electronics Engineering
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      Comprehensive lower bounds on sequential prediction

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      Author
      Vanlı, N. Denizcan
      Sayın, Muhammed O.
      Ergüt, S.
      Kozat, Süleyman S.
      Date
      2014-09
      Source Title
      European Signal Processing Conference
      Print ISSN
      2219-5491
      Publisher
      IEEE
      Pages
      1193 - 1196
      Language
      English
      Type
      Conference Paper
      Item Usage Stats
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      Abstract
      We study the problem of sequential prediction of real-valued sequences under the squared error loss function. While refraining from any statistical and structural assumptions on the underlying sequence, we introduce a competitive approach to this problem and compare the performance of a sequential algorithm with respect to the large and continuous class of parametric predictors. We define the performance difference between a sequential algorithm and the best parametric predictor as regret, and introduce a guaranteed worst-case lower bounds to this relative performance measure. In particular, we prove that for any sequential algorithm, there always exists a sequence for which this regret is lower bounded by zero. We then extend this result by showing that the prediction problem can be transformed into a parameter estimation problem if the class of parametric predictors satisfy a certain property, and provide a comprehensive lower bound to this case.
      Keywords
      Lower bound
      Sequential prediction
      Worst-case performance
      Forecasting
      Sequential switching
      Signal processing
      Parameter estimation problems
      Relative performance
      Sequential algorithm
      Sequential prediction
      Squared error loss functions
      Structural assumption
      Parameter estimation
      Permalink
      http://hdl.handle.net/11693/27868
      Published Version (Please cite this version)
      https://ieeexplore.ieee.org/document/6952418
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      • Department of Electrical and Electronics Engineering 3524
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