Dimension-free PAC-Bayesian bounds for the estimation of the mean of a random vector

Olivier Catoni (1) , Ilaria Giulini (2)

1 CREST - Centre de Recherche en Économie et Statistique
2 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

In this paper, we present a new estimator of the mean of a random vector, computed by applying some threshold function to the norm. Non asymptotic dimension-free almost sub-Gaussian bounds are proved under weak moment assumptions, using PAC-Bayesian inequalities.

Domaines: Mathématiques [math]

Olivier Catoni, Ilaria Giulini. Dimension-free PAC-Bayesian bounds for the estimation of the mean of a random vector. 2021. ⟨hal-03196139⟩