Axiomatization of an exponential similarity function

Antoine Billot (), Itzhak Gilboa () and David Schmeidler ()

Mathematical Social Sciences, 2008, vol. 55, issue 2, pages 107-115

Abstract: An individual is asked to assess a real-valued variable y based on certain characteristics x = (x1,..., xm), and on a database consisting of n observations of (x1,..., xm, 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, yn+1s, be the weighted average of all previously observed values yi, where the weight of yi is the similarity between the vector xn+11,..., xn+1m, associated with yn+1, and the previously observed vector, xi1,..., xim. This paper axiomatizes, in terms of the prediction yn+1, a similarity function that is a (decreasing) exponential in a norm of the difference between the two vectors compared.

Date: 2008
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Related works:
Working Paper: Axiomatization of an Exponential Similarity Function (2004)
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Persistent link: http://EconPapers.repec.org/RePEc:eee:matsoc:v:55:y:2008:i:2:p:107-115

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