Exponential bounds for multivariate self-normalized sums

Patrice Bertail (1, 2) , Emmanuelle Gautherat (2) , Hugo Harari-Kermadec (2, 3)

1 MODAL'X - Modélisation aléatoire de Paris X
2 CREST - Centre de Recherche en Économie et Statistique
3 ENS Cachan - École normale supérieure - Cachan

In a non-parametric framework, we establish some non-asymptotic bounds for self-normalized sums and quadratic forms in the multivariate case for symmetric and general random variables. This bounds are entirely explicit and essentially depends in the general case on the kurtosis of the Euclidean norm of the standardized random variables.

Mots clés: Exponential bounds; self normalized sums; quadratic forms; multivariate

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Probabilités [math.PR]

Patrice Bertail, Emmanuelle Gautherat, Hugo Harari-Kermadec. Exponential bounds for multivariate self-normalized sums. 2008. ⟨hal-00333999⟩