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A similarity-based approach to prediction

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  • Gilboa, Itzhak
  • Lieberman, Offer
  • Schmeidler, David

Abstract

Assume we are asked to predict a real-valued variable yt based on certain characteristics , and on a database consisting of 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, , 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 , associated with yt, and the previously observed vector, . 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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 162 (2011)
Issue (Month): 1 (May)
Pages: 124-131

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Handle: RePEc:eee:econom:v:162:y:2011:i:1:p:124-131

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Density estimation Empirical similarity Kernel Spatial models;

References

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  1. Itzhak Gilboa & David Schmeidler, 2002. "Inductive Inference: An Axiomatic Approach," Levine's Working Paper Archive 391749000000000544, David K. Levine.
  2. 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.
  3. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521003117.
  4. Billot, Antoine & Gilboa, Itzhak & Schmeidler, David, 2008. "Axiomatization of an exponential similarity function," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 107-115, March.
  5. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2006. "Empirical Similarity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 433-444, August.
  6. Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2005. "Probabilities as Similarity-Weighted Frequencies," Econometrica, Econometric Society, vol. 73(4), pages 1125-1136, 07.
  7. Gabrielle Gayer & Itzhak Gilboa & Offer Lieberman, 2004. "Rule-Based and Case-Based Reasoning in Housing Prices," Levine's Bibliography 122247000000000672, UCLA Department of Economics.
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Citations

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Cited by:
  1. 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.
  2. 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.
  3. Teitelbaum, Joshua C., 2013. "Asymmetric empirical similarity," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 346-351.
  4. Joerg Bleile, 2014. "Cautious Belief Formation," Working Papers 507, Bielefeld University, Center for Mathematical Economics.

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