Mass localization

Thibaut Le Gouic (1)

1 I2M - Institut de Mathématiques de Marseille

For a given class F of closed sets of a measured metric space (E, d, µ), we want to find the smallest element B of the class F such that µ(B) ≥ 1 − α, for a given 0 < α < 1. This set B localizes the mass of µ. Replacing the measure µ by the empirical measure µn gives an empirical smallest set Bn. The article introduces a formal definition of small sets (and their size) and study the convergence of the sets Bn to B and of their size.

Domaines: Statistiques [math.ST]

Thibaut Le Gouic. Mass localization. 2015. ⟨hal-01163389⟩