Prediction by quantization of a conditional distribution

Jean-Michel Loubes (1) , Bruno Pelletier (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IRMAR - Institut de Recherche Mathématique de Rennes

We consider the problem of quantizing the conditional distribution of a random variable Y given a random vector X. We propose an empirical quantizer defined by combining the principles of k-means clustering with the nonparametric smoothing technique of k-nearest neighbors. We provide an asymptotic analysis of the estimate and we derive a bound on the error rate of the quantizer. The proposed methodology is illustrated on simulated examples and on a speed-flow traffic data set used in the context of road traffic forecasting.

Mots clés: Regression analysis; vector quantization; nonparametric statistics; clustering; k-means

Domaines: Statistiques [math.ST]

Jean-Michel Loubes, Bruno Pelletier. Prediction by quantization of a conditional distribution. 2016. ⟨hal-01299554v1⟩