An agent is asked to assess a real-valued variable Y p based on certain characteristics X p = (X p -super-1, ..., X p -super-m), and on a database consisting of X i -super-1, ... X i -super-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, È² p -super-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 -super-1, ..., X p -super-m, associated with Y p , and the previously observed vector, X i -super-1, ..., X i -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.
If you experience problems downloading a file, check if you have the proper application to view it first. 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.
Volume (Year): 88 (2006)
Issue (Month): 3 (August)
|Contact details of provider:|| Web page: http://mitpress.mit.edu/journals/|
|Order Information:||Web: http://mitpress.mit.edu/journal-home.tcl?issn=00346535|
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.:
- Billot, Antoine & Gilboa, Itzhak & Schmeidler, David, 2008.
"Axiomatization of an exponential similarity function,"
Mathematical Social Sciences,
Elsevier, vol. 55(2), pages 107-115, March.
- Antoine Billot & Itzhak Gilboa & David Schmeidler, 2004. "Axiomatization of an Exponential Similarity Function," Cowles Foundation Discussion Papers 1485, Cowles Foundation for Research in Economics, Yale University.
- Antoine Billot & Itzhak Gilboa & David Schmeidler, 2008. "Axiomatization of an exponential similarity function," Post-Print hal-00463265, HAL.
- Itzhak Gilboa & David Schmeidler, 1995. "Case-Based Decision Theory," The Quarterly Journal of Economics, Oxford University Press, vol. 110(3), pages 605-639.
- Itzhak Gilboa & David Schmeidler, 1992. "Case-Based Decision Theory," Discussion Papers 994, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Itzhak Gilboa & David Schmeidler, 1995. "Case-Based Decision Theory," Post-Print hal-00753144, HAL.
- 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.
- Gabrielle Gayer & Itzhak Gilboa & Offer Lieberman, 2004. "Rule-Based and Case-Based Reasoning in Housing Prices," Levine's Bibliography 122247000000000672, UCLA Department of Economics.
- Itzhak Gilboa & Gabrielle Gayer & O. Lieberman, 2007. "Rule-Based and Case-Based Reasoning in Housing Prices," Post-Print hal-00481229, HAL.
- Gabrielle Gayer & Itzhak Gilboa & Offer Lieberman, 2004. "Rule-Based and Case-Based Reasoning in Housing Prices," Cowles Foundation Discussion Papers 1493, Cowles Foundation for Research in Economics, Yale University.
- Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2003. "Probabilities: Frequencies Viewed in Perspective," Levine's Bibliography 666156000000000295, UCLA Department of Economics.
- Antoine Billot & Itzhak Gilboa & David Schmeidler, 2004. "An Axiomatization of an Exponential Similarity Function," Levine's Bibliography 122247000000000678, UCLA Department of Economics. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:tpr:restat:v:88:y:2006:i:3:p:433-444. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Kristin Waites)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.