CFDP 1485

Axiomatization of an Exponential Similarity Function

Author(s): 

Publication Date: October 2004

Pages: 10

Abstract: 

An agent 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, ysn+1, be the weighted average of all previously observed values yi, where the weight of yi is the similarity between the vector x1n+1,…,xmn+1, associated with yn+1, and the previously observed vector, x1i,…,xmi. 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.

Keywords: 

Similarity, Exponential

JEL Classification Codes:  C8, D8