A similarity-based approach to prediction

Itzhak Gilboa, Offer Lieberman, David Schmeidler

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

Abstract

Assume we are asked to predict a real-valued variable yt based on certain characteristics xt=(xt1,...,x td), and on a database consisting of (xi 1,...,xid,yi) for i=1,...,n. Analogical reasoning suggests to combine past observations of x and y with the current values of x to generate an assessment of y by similarity-weighted averaging. Specifically, the predicted value of y, yts, is the weighted average of all previously observed values yi, where the weight of y i, for every i=1,...,n, is the similarity between the vector x t1,...,xtd, associated with y t, and the previously observed vector, xi 1,...,xid. The "empirical similarity" approach suggests estimation of the similarity function from past data. We discuss this approach as a statistical method of prediction, study its relationship to the statistical literature, and extend it to the estimation of probabilities and of density functions.

Original languageEnglish
Pages (from-to)124-131
Number of pages8
JournalJournal of Econometrics
Volume162
Issue number1
DOIs
StatePublished - May 2011
Externally publishedYes

Keywords

  • Density estimation
  • Empirical similarity
  • Kernel
  • Spatial models

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