IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-00609179.html
   My bibliography  Save this paper

A similarity-based approach to prediction

Author

Listed:
  • Itzhak Gilboa

    () (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

  • O. Lieberman
  • David Schmeidler

    (Department of Cell and Developmental Biology - Tel Aviv University [Tel Aviv] - Sackler Faculty of Medicine)

Abstract

Assume we are asked to predict a real-valued variable yt based on certain characteristics View the MathML source, and on a database consisting of View the MathML source for i=1,...,n. Analogical reasoning suggests to combine past observations of x and y with the current values of x to generate an assessment of y by similarity-weighted averaging. Specifically, the predicted value of y, View the MathML source, is the weighted average of all previously observed values yi, where the weight of yi, for every i=1,...,n, is the similarity between the vector View the MathML source, associated with yt, and the previously observed vector, View the MathML source. The "empirical similarity" approach suggests estimation of the similarity function from past data. We discuss this approach as a statistical method of prediction, study its relationship to the statistical literature, and extend it to the estimation of probabilities and of density functions.

Suggested Citation

  • Itzhak Gilboa & O. Lieberman & David Schmeidler, 2011. "A similarity-based approach to prediction," Post-Print hal-00609179, HAL.
  • Handle: RePEc:hal:journl:hal-00609179
    DOI: 10.1016/j.jeconom.2009.10.015
    Note: View the original document on HAL open archive server: https://hal-hec.archives-ouvertes.fr/hal-00609179
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Itzhak Gilboa & David Schmeidler, 2003. "Inductive Inference: An Axiomatic Approach," Econometrica, Econometric Society, vol. 71(1), pages 1-26, January.
    2. Billot, Antoine & Gilboa, Itzhak & Schmeidler, David, 2008. "Axiomatization of an exponential similarity function," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 107-115, March.
    3. L. Yang & R. Tschernig, 1999. "Multivariate bandwidth selection for local linear regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 793-815.
    4. Gayer Gabrielle & Gilboa Itzhak & Lieberman Offer, 2007. "Rule-Based and Case-Based Reasoning in Housing Prices," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-37, April.
    5. Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2005. "Probabilities as Similarity-Weighted Frequencies," Econometrica, Econometric Society, vol. 73(4), pages 1125-1136, July.
    6. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2006. "Empirical Similarity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 433-444, August.
    7. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521802345, August.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Kinjo Keita & Sugawara Shinya, 2016. "Predicting Empirical Patterns in Viewing Japanese TV Dramas Using Case-Based Decision Theory," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 16(2), pages 679-709, June.
    2. Golosnoy, Vasyl & Hamid, Alain & Okhrin, Yarema, 2014. "The empirical similarity approach for volatility prediction," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 321-329.
    3. Kapetanios, George & Mitchell, James & Shin, Yongcheol, 2014. "A nonlinear panel data model of cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 179(2), pages 134-157.
    4. Oscar Melo & Carlos Melo & Jorge Mateu, 2015. "Distance-based beta regression for prediction of mutual funds," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 83-106, January.
    5. Han Bleichrodt & Martin Filko & Amit Kothiyal & Peter P. Wakker, 2017. "Making Case-Based Decision Theory Directly Observable," American Economic Journal: Microeconomics, American Economic Association, vol. 9(1), pages 123-151, February.
    6. Teitelbaum, Joshua C., 2013. "Asymmetric empirical similarity," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 346-351.
    7. Bleile, Jörg, 2016. "Cautious Belief Formation," Center for Mathematical Economics Working Papers 507, Center for Mathematical Economics, Bielefeld University.

    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:hal:journl:hal-00609179. 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: (CCSD). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with 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.