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Axiomatization of an Exponential Similarity Function

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  • Antoine Billot

    (Universite de Paris II)

  • Itzhak Gilboa

    (School of Economics, Tel Aviv Univ.)

  • David Schmeidler

    (School of Mathematical Sciences, Tel Aviv Univ.)

Abstract

An agent is asked to assess a real-valued variable y based on certain characteristics x=(x^{1},...,x^{m}), and on a database consisting of n observations of (x^{1},...,x^{m},y). 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, y_{n+1}^{s}, be the weighted average of all previously observed values y_{i}, where the weight of y_{i} is the similarity between the vector x_{n+1}^{1},...,x_{n+1}^{m}, associated with y_{n+1}, and the previously observed vector, x_{i}^{1},...,x_{i}^{m}. This paper axiomatizes, in terms of the prediction y_{n+1}, a similarity function that is a (decreasing) exponential in a norm of the difference between the two vectors compared.

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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1485.

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Length: 10 pages
Date of creation: Sep 2004
Date of revision:
Publication status: Published in Mathematical Social Sciences (2008), 55: 107-115
Handle: RePEc:cwl:cwldpp:1485

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Keywords: Similarity; exponential;

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References

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  1. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2004. "Empirical Similarity," Cowles Foundation Discussion Papers 1486, Cowles Foundation for Research in Economics, Yale University.
  2. Itzhak Gilboa & David Schmeidler, 2002. "Inductive Inference: An Axiomatic Approach," NajEcon Working Paper Reviews 391749000000000544, www.najecon.org.
  3. Antoine Billot & Itzhak Gilboa & David Schmeidler & Dov Samet, 2004. "Probabilities as Similarity-Weighted Frequencies," Cowles Foundation Discussion Papers 1492, Cowles Foundation for Research in Economics, Yale University.
  4. Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2003. "Probabilities: Frequencies Viewed in Perspective," Levine's Bibliography 666156000000000295, UCLA Department of Economics.
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Cited by:
  1. Gayer, Gabrielle, 2010. "Perception of probabilities in situations of risk: A case based approach," Games and Economic Behavior, Elsevier, vol. 68(1), pages 130-143, January.
  2. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2004. "Empirical Similarity," Cowles Foundation Discussion Papers 1486, Cowles Foundation for Research in Economics, Yale University.
  3. Antoine Billot & Itzhak Gilboa & David Schmeidler & Dov Samet, 2004. "Probabilities as Similarity-Weighted Frequencies," Cowles Foundation Discussion Papers 1492, Cowles Foundation for Research in Economics, Yale University.
  4. 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.
  5. Pape, Andreas & Kurtz, Kenneth, 2013. "Evaluating Case-based Decision Theory: Predicting Empirical Patterns of Human Classification Learning (Extensions)," MPRA Paper 45206, University Library of Munich, Germany.
  6. Pape, Andreas Duus & Kurtz, Kenneth J., 2013. "Evaluating case-based decision theory: Predicting empirical patterns of human classification learning," Games and Economic Behavior, Elsevier, vol. 82(C), pages 52-65.
  7. Teitelbaum, Joshua C., 2013. "Asymmetric empirical similarity," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 346-351.
  8. Wolfgang Ossadnik & Dirk Wilmsmann & Benedikt Niemann, 2013. "Experimental evidence on case-based decision theory," Theory and Decision, Springer, vol. 75(2), pages 211-232, August.
  9. Gilboa, Itzhak & Lieberman, Offer & Schmeidler, David, 2011. "A similarity-based approach to prediction," Journal of Econometrics, Elsevier, vol. 162(1), pages 124-131, May.

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