IDEAS home Printed from https://ideas.repec.org/p/upf/upfgen/324.html
   My bibliography  Save this paper

On prediction of individual sequences

Author

Listed:

Abstract

Sequential randomized prediction of an arbitrary binary sequence is investigated. No assumption is made on the mechanism of generating the bit sequence. The goal of the predictor is to minimize its relative loss, i.e., to make (almost) as few mistakes as the best ``expert'' in a fixed, possibly infinite, set of experts. We point out a surprising connection between this prediction problem and empirical process theory. First, in the special case of static (memoryless) experts, we completely characterize the minimax relative loss in terms of the maximum of an associated Rademacher process. Then we show general upper and lower bounds on the minimax relative loss in terms of the geometry of the class of experts. As main examples, we determine the exact order of magnitude of the minimax relative loss for the class of autoregressive linear predictors and for the class of Markov experts.

Suggested Citation

  • Nicolo Cesa Bianchi & Gábor Lugosi, 1998. "On prediction of individual sequences," Economics Working Papers 324, Department of Economics and Business, Universitat Pompeu Fabra.
  • Handle: RePEc:upf:upfgen:324
    as

    Download full text from publisher

    File URL: https://econ-papers.upf.edu/papers/324.pdf
    File Function: Whole Paper
    Download Restriction: no

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gábor Lugosi & Shie Mannor & Gilles Stoltz, 2008. "Strategies for Prediction Under Imperfect Monitoring," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 513-528, August.
    2. A. Borodin & R. El-Yaniv & V. Gogan, 2011. "Can We Learn to Beat the Best Stock," Papers 1107.0036, arXiv.org.
    3. Sancetta, A., 2005. "Forecasting Distributions with Experts Advice," Cambridge Working Papers in Economics 0517, Faculty of Economics, University of Cambridge.
    4. Sancetta, Alessio, 2007. "Online forecast combinations of distributions: Worst case bounds," Journal of Econometrics, Elsevier, vol. 141(2), pages 621-651, December.

    More about this item

    Keywords

    Universal prediction; prediction with experts; absolute loss; empirical processes; covering numbers; finite-state machines;

    JEL classification:

    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:upf:upfgen:324. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: http://www.econ.upf.edu/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.