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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.

Suggested Citation

  • Gilboa, Itzhak & Lieberman, Offer & Schmeidler, David, 2011. "A similarity-based approach to prediction," Journal of Econometrics, Elsevier, vol. 162(1), pages 124-131, May.
  • Handle: RePEc:eee:econom:v:162:y:2011:i:1:p:124-131
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    References listed on IDEAS

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    1. Itzhak Gilboa & David Schmeidler, 2003. "Inductive Inference: An Axiomatic Approach," Econometrica, Econometric Society, vol. 71(1), pages 1-26, January.
    2. Antoine Billot & Itzhak Gilboa & David Schmeidler, 2012. "Axiomatization of an Exponential Similarity Function," World Scientific Book Chapters, in: Case-Based Predictions An Axiomatic Approach to Prediction, Classification and Statistical Learning, chapter 10, pages 245-257, World Scientific Publishing Co. Pte. Ltd..
    3. Itzhak Gilboa & David Schmeidler, 1995. "Case-Based Decision Theory," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(3), pages 605-639.
    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, 2012. "Probabilities as Similarity-Weighted Frequencies," World Scientific Book Chapters, in: Case-Based Predictions An Axiomatic Approach to Prediction, Classification and Statistical Learning, chapter 7, pages 169-184, World Scientific Publishing Co. Pte. Ltd..
    6. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521802345.
    7. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2012. "Empirical Similarity," World Scientific Book Chapters, in: Case-Based Predictions An Axiomatic Approach to Prediction, Classification and Statistical Learning, chapter 9, pages 211-243, World Scientific Publishing Co. Pte. Ltd..
    8. 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.
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    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. Y. Dendramis & G. Kapetanios & M. Marcellino, 2020. "A similarity‐based approach for macroeconomic forecasting," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 801-827, June.
    4. 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.
    5. Chiang, Mi-Hsiu & Chiu, Hsin-Yu & Kuo, Wei-Yu, 2021. "Predictive ability of similarity-based futures trading strategies," Pacific-Basin Finance Journal, Elsevier, vol. 68(C).
    6. Rossi, Francesca & Lieberman, Offer, 2023. "Spatial autoregressions with an extended parameter space and similarity-based weights," Journal of Econometrics, Elsevier, vol. 235(2), pages 1770-1798.
    7. Ralf Becker & Adam Clements & Robert O'Neill, 2018. "A Multivariate Kernel Approach to Forecasting the Variance Covariance of Stock Market Returns," Econometrics, MDPI, vol. 6(1), pages 1-27, February.
    8. Pablo Guerróon‐Quintana & Molin Zhong, 2023. "Macroeconomic forecasting in times of crises," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(3), pages 295-320, April.
    9. 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.
    10. 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.
    11. Teitelbaum, Joshua C., 2013. "Asymmetric empirical similarity," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 346-351.
    12. Bleile, Jörg, 2016. "Cautious Belief Formation," Center for Mathematical Economics Working Papers 507, Center for Mathematical Economics, Bielefeld University.

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