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Empirical Similarity

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Author Info
Itzhak Gilboa (Tel-Aviv University, HEC, and Yale University)
Offer Lieberman (The Technion)
David Schmeidler (Tel-Aviv University and The Ohio State University)

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Abstract

An agent is asked to assess a real-valued variable Yp based on certain characteristics Xp = (Xp-super-1, ..., Xp-super-m), and on a database consisting of Xi-super-1, ... Xi-super-m, Yi) for i = 1, ..., n. A possible approach to combine past observations of X and Y with the current values of X to generate an assessment of Y is similarity-weighted averaging. It suggests that the predicted value of Y, Ȳp-super-s, be 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 Xp-super-1, ..., Xp-super-m, associated with Yp, and the previously observed vector, Xi-super-1, ..., Xi-super-m. We axiomatize this rule. We assume that, given every database, a predictor has a ranking over possible values, and we show that certain reasonable conditions on these rankings imply that they are determined by the proximity to a similarity-weighted average for a certain similarity function. The axiomatization does not suggest a particular similarity function, or even a particular form of this function. We therefore proceed to suggest that the similarity function be estimated from past observations.We develop tools of statistical inference for parametric estimation of the similarity function, for the case of a continuous as well as a discrete variable. Finally, we discuss the relationship of the proposed method to other methods of estimation and prediction. Copyright by the President and Fellows of Harvard College and the Massachusetts Institute of Technology.

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File URL: http://www.mitpressjournals.org/doi/pdfplus/10.1162/rest.88.3.433
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Publisher Info
Article provided by MIT Press in its journal The Review of Economics and Statistics.

Volume (Year): 88 (2006)
Issue (Month): 3 (09)
Pages: 433-444
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Handle: RePEc:tpr:restat:v:88:y:2006:i:3:p:433-444

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Antoine Billot & Itzhak Gilboa & David Schmeidler, 2004. "An Axiomatization of an Exponential Similarity Function," Levine's Bibliography 122247000000000678, UCLA Department of Economics. [Downloadable!]
  2. Antoine Billot & Itzhak Gilboa & David Schmeidler, 2004. "Axiomatization of an Exponential Similarity Function," Cowles Foundation Discussion Papers 1485, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  3. Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2003. "Probabilities: Frequencies Viewed in Perspective," Levine's Bibliography 666156000000000295, UCLA Department of Economics. [Downloadable!]
  4. Gabrielle Gayer & Itzhak Gilboa & Offer Lieberman, 2004. "Rule-Based and Case-Based Reasoning in Housing Prices," Levine's Bibliography 122247000000000672, UCLA Department of Economics. [Downloadable!]
    Other versions:
  5. Gilboa, Itzhak & Schmeidler, David, 1995. "Case-Based Decision Theory," The Quarterly Journal of Economics, MIT Press, vol. 110(3), pages 605-39, August. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. repec:bep:theadv:v:7:y:2007:i:1:p:1284-1284 is not listed on IDEAS
  2. Jürgen Eichberger & Ani Guerdjikova, 2008. "Multiple Priors as Similarity Weighted Frequencies," Working Papers 0470, University of Heidelberg, Department of Economics, revised Jul 2008. [Downloadable!]
  3. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2007. "On the Definition of Objective Probabilities by Empirical Similarity," Levine's Bibliography 843644000000000363, UCLA Department of Economics. [Downloadable!]
  4. Eichberger, Jurgen & Guerdjikova, Ani, 2007. "Multiple Priors as Similarity Weighted Frequencies," Working Papers 07-03, Cornell University, Center for Analytic Economics. [Downloadable!]
  5. Antoine Billot & Itzhak Gilboa & David Schmeidler, 2004. "An Axiomatization of an Exponential Similarity Function," Levine's Bibliography 122247000000000678, UCLA Department of Economics. [Downloadable!]
  6. Itzhak Gilboa, 2009. "Questions in Decision Theory," Levine's Working Paper Archive 814577000000000335, David K. Levine. [Downloadable!]
  7. Eichberger, Jürgen & Guerdjikova, Ani, 2008. "Multiple Priors as Similarity Weighted Frequencies," Sonderforschungsbereich 504 Publications 08-07, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim. [Downloadable!]
  8. Antoine Billot & Itzhak Gilboa & David Schmeidler, 2004. "Axiomatization of an Exponential Similarity Function," Cowles Foundation Discussion Papers 1485, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  9. Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2007. "Probability and Uncertainty in Economic Modeling, Second Version," PIER Working Paper Archive 08-002, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 28 Jan 2008. [Downloadable!]
  10. Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2004. "Probabilities as Similarity-Weighted Frequencies," Levine's Bibliography 122247000000000696, UCLA Department of Economics. [Downloadable!]
    Other versions:
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