TY - JOUR

T1 - A similarity-based approach to prediction

AU - Gilboa, Itzhak

AU - Lieberman, Offer

AU - Schmeidler, David

PY - 2011/5

Y1 - 2011/5

N2 - 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.

AB - 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.

KW - Density estimation

KW - Empirical similarity

KW - Kernel

KW - Spatial models

UR - http://www.scopus.com/inward/record.url?scp=79952992533&partnerID=8YFLogxK

U2 - 10.1016/j.jeconom.2009.10.015

DO - 10.1016/j.jeconom.2009.10.015

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AN - SCOPUS:79952992533

SN - 0304-4076

VL - 162

SP - 124

EP - 131

JO - Journal of Econometrics

JF - Journal of Econometrics

IS - 1

ER -