Empirical Similarity

Itzhak Gilboa, Offer Lieberman and David Schmeidler
Additional contact information
Offer Lieberman: Technion-Israel Institute of Technology

No 1486, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: An agent is asked to assess a real-valued variable Y_{p} based on certain characteristics X_{p} = (X_{p}^{1},...,X_{p}^{m}), and on a database consisting (X_{i}^{1},...,X_{i}^{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, Y_{p}^{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}^{1},...,X_{p}^{m}, associated with Y_{p}, and the previously observed vector, X_{i}^{1},...,X_{i}^{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 functional 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.

Keywords: Similarity; estimation (search for similar items in EconPapers)
JEL-codes: C1 C8 D8 (search for similar items in EconPapers)
Pages: 38 pages
Date: 2004-09
New Economics Papers: this item is included in nep-hpe
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

Published in Review of Economics and Statistics (2006), 88(3): 433-444

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Related works:
Chapter: Empirical Similarity (2012)
Journal Article: Empirical Similarity (2006)
Working Paper: Empirical Similarity (2006)
Working Paper: Empirical Similarity (2004)
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