Itzhak Gilboa (Tel-Aviv University, HEC, and Yale University) Offer Lieberman (The Technion) David Schmeidler (Tel-Aviv University and The Ohio State University)
Additional information is available for the following
registered author(s):
An agent is asked to assess a real-valued variable Yp based on certain characteristics Xp = (Xp-super-1, ..., Xp-super-m), and on a database consisting of Xi-super-1, ... Xi-super-m, Yi) 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, Ȳp-super-s, be 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 Xp-super-1, ..., Xp-super-m, associated with Yp, and the previously observed vector, Xi-super-1, ..., Xi-super-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 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. Copyright by the President and Fellows of Harvard College and the Massachusetts Institute of Technology.
Download Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. In case of further problems read
the IDEAS help
page. Note that these files are not on the IDEAS
site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2004.
"Empirical Similarity,"
Levine's Bibliography
122247000000000684, UCLA Department of Economics.
[Downloadable!]
References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
Itzhak Gilboa & David Schmeidler, 1992.
"Case-Based Decision Theory,"
Discussion Papers
994, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
[Downloadable!]
Cited by: (explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)
repec:bep:theadv:v:7:y:2007:i:1:p:1284-1284 is not listed on IDEAS