A Similarity-Based Approach to Prediction

I. GILBOA, O. Lieberman, D. Schmeidler

Journal of Econometrics

mai 2011, vol. 162, n°1, pp.124-131

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)

Assume we are asked to predict a real-valued variable yt based on certain characteristics xt = (x1t , . . . , xdt), and on a database consisting of (x1i, . . . , xdi , 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, yst , is 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 x1t, . . . , xdt, associated with yt , and the previously observed vector, x1i , . . . , xdi. 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.Keywords:Density estimationEmpirical similarityKernelSpatial models