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Abstract

An agent is asked to assess a real-valued variable Y p based on certain characteristics X p = (X p-super-1, ..., X p-super-m), and on a database consisting of X i-super-1, ... X i-super-m, Y i) 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, Ȳ p-super-s, be the weighted average of all previously observed values Y i, where the weight of Y i for every i = 1, ..., n, is the similarity between the vector X p-super-1, ..., X p-super-m, associated with Y p, and the previously observed vector, X i-super-1, ..., X i-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/pdf/10.1162/rest.88.3.433
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Bibliographic Info

Article provided by MIT Press in its journal The Review of Economics and Statistics.

Volume (Year): 88 (2006)
Issue (Month): 3 (August)
Pages: 433-444

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Handle: RePEc:tpr:restat:v:88:y:2006:i:3:p:433-444

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Web page: http://mitpress.mit.edu/journals/

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Find related papers by JEL classification:

• C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
• C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs
• D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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1. Billot, Antoine & Gilboa, Itzhak & Schmeidler, David, 2008. "Axiomatization of an exponential similarity function," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 107-115, March.
   
   • Antoine Billot & Itzhak Gilboa & David Schmeidler, 2004. "Axiomatization of an Exponential Similarity Function," Cowles Foundation Discussion Papers 1485, Cowles Foundation for Research in Economics, Yale University.
2. Itzhak Gilboa & David Schmeidler, 1992. "Case-Based Decision Theory," Discussion Papers 994, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
   
   • Gilboa, Itzhak & Schmeidler, David, 1995. "Case-Based Decision Theory," The Quarterly Journal of Economics, MIT Press, vol. 110(3), pages 605-39, August.
3. Gabrielle Gayer & Itzhak Gilboa & Offer Lieberman, 2004. "Rule-Based and Case-Based Reasoning in Housing Prices," Cowles Foundation Discussion Papers 1493, Cowles Foundation for Research in Economics, Yale University.
   
   • Gabrielle Gayer & Itzhak Gilboa & Offer Lieberman, 2007. "Rule-Based and Case-Based Reasoning in Housing Prices," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 10.
   • Gabrielle Gayer & Itzhak Gilboa & Offer Lieberman, 2004. "Rule-Based and Case-Based Reasoning in Housing Prices," Levine's Bibliography 122247000000000672, UCLA Department of Economics.
4. Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2003. "Probabilities: Frequencies Viewed in Perspective," Levine's Bibliography 666156000000000295, UCLA Department of Economics.
5. Antoine Billot & Itzhak Gilboa & David Schmeidler, 2004. "An Axiomatization of an Exponential Similarity Function," Levine's Bibliography 122247000000000678, UCLA Department of Economics.

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Cited by:

1. Gilboa, Itzhak & Lieberman, Offer & Schmeidler, David, 2011. "A similarity-based approach to prediction," Journal of Econometrics, Elsevier, vol. 162(1), pages 124-131, May.
2. Jürgen Eichberger & Ani Guerdjikova, 2008. "Multiple Priors as Similarity Weighted Frequencies," Working Papers 0470, University of Heidelberg, Department of Economics, revised Jul 2008.
   
   • 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.
   • Eichberger, Jurgen & Guerdjikova, Ani, 2007. "Multiple Priors as Similarity Weighted Frequencies," Working Papers 07-03, Cornell University, Center for Analytic Economics.
3. Eichberger, Jürgen & Guerdjikova, Ani, 2010. "Case-based belief formation under ambiguity," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 161-177, November.
4. Itzhak Gilboa & Andrew Postlewaite & Larry Samuelson & David Schmeidler, 2011. "Economic Models as Analogies, Second Version," PIER Working Paper Archive 12-030, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 31 Jul 2012.
5. Itzhak Gilboa, 2009. "Questions in Decision Theory," Levine's Working Paper Archive 814577000000000335, David K. Levine.
   
   • Itzhak Gilboa, 2010. "Questions in Decision Theory," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 1-19, 09.
6. George Kapetanios & James Mitchell & Yongcheol Shin, 2010. "A Nonlinear Panel Model of Cross-sectional Dependence," Working Papers 673, Queen Mary, University of London, School of Economics and Finance.
7. 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.
   
   • Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2005. "Probabilities as Similarity-Weighted Frequencies," Econometrica, Econometric Society, vol. 73(4), pages 1125-1136, 07.
   • Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2004. "Probabilities as Similarity-Weighted Frequencies," Levine's Bibliography 122247000000000696, UCLA Department of Economics.
8. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2007. "On the Definition of Objective Probabilities by Empirical Similarity," Levine's Bibliography 843644000000000363, UCLA Department of Economics.
9. 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.
10. I. Gilboa & A. W. Postlewaite & D. Schmeidler., 2009. "Probability and Uncertainty in Economic Modeling," VOPROSY ECONOMIKI, N.P. Redaktsiya zhurnala "Voprosy Economiki", vol. 10.
    
    • Itzhak Gilboa & Andrew W. Postlewaite & David Schmeidler, 2008. "Probability and Uncertainty in Economic Modeling," Journal of Economic Perspectives, American Economic Association, vol. 22(3), pages 173-88, Summer.
11. Antoine Billot & Itzhak Gilboa & David Schmeidler, 2004. "An Axiomatization of an Exponential Similarity Function," Levine's Bibliography 122247000000000678, UCLA Department of Economics.
12. Billot, Antoine & Gilboa, Itzhak & Schmeidler, David, 2008. "Axiomatization of an exponential similarity function," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 107-115, March.
    
    • Antoine Billot & Itzhak Gilboa & David Schmeidler, 2004. "Axiomatization of an Exponential Similarity Function," Cowles Foundation Discussion Papers 1485, Cowles Foundation for Research in Economics, Yale University.
13. Itzhak Gilboa & Andrew Postlewaite & Larry Samuelson & David Schmeidler, 2012. "Economic Models as Analogies, Third Version," PIER Working Paper Archive 13-007, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 27 Jan 2013.
14. Gilboa, Itzhak & Schmeidler, David, 2010. "Simplicity and likelihood: An axiomatic approach," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1757-1775, September.
    
    • Itzhak Gilboa & David Schmeidler, 2008. "Simplicity and Likelihood: An Axiomatic Approach," Levine's Working Paper Archive 122247000000001970, David K. Levine.
15. 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.
16. Mohlin, Erik, 2009. "Optimal Categorization," Working Paper Series in Economics and Finance 721, Stockholm School of Economics, revised 08 Jul 2009.
17. Ani Guerdjikova & Jürgen Eichberger, 2012. "Ambiguity, Data and Preferences for Information - A Case-Based Approach," THEMA Working Papers 2012-45 Classification-Je, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.

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